(CNN) More than half the nation's governors say they oppose letting Syrian refugees into their states, although the final say on this contentious immigration issue will fall to the federal government.

States protesting the admission of refugees range from Alabama and Georgia, to Texas and Arizona, to Michigan and Illinois, to Maine and New Hampshire. Among these 31 states, all but one have Republican governors.

The announcements came after authorities revealed that at least one of the suspects believed to be involved in the Paris terrorist attacks entered Europe among the current wave of Syrian refugees. He had falsely identified himself as a Syrian named Ahmad al Muhammad and was allowed to enter Greece in early October.

French security forces move people in the area of Rue Bichat in the 10th District. A witness told BFMTV that firefighters were on the scene to treat the injured.

French security forces move people in the area of Rue Bichat in the 10th District. A witness told BFMTV that firefighters were on the scene to treat the injured.

Rescue workers and medics tend to victims at the scene of one of the shootings, a restaurant in the 10th District. Attackers reportedly used AK-47 automatic weapons in separate attacks across Paris, and there were explosions at the Stade de France.

Rescue workers and medics tend to victims at the scene of one of the shootings, a restaurant in the 10th District. Attackers reportedly used AK-47 automatic weapons in separate attacks across Paris, and there were explosions at the Stade de France.

People leave the Stade de France after explosions were heard near the stadium during a soccer match between France and Germany on Friday. Paris Deputy Mayor Patrick Klugman told CNN President Francois Hollande was at the match and was evacuated at halftime.

People leave the Stade de France after explosions were heard near the stadium during a soccer match between France and Germany on Friday. Paris Deputy Mayor Patrick Klugman told CNN President Francois Hollande was at the match and was evacuated at halftime.

French security forces rush in as people are evacuated in the area of Rue Bichat in the 10th District of Paris.

French security forces rush in as people are evacuated in the area of Rue Bichat in the 10th District of Paris.

Spectators gather on the field of the Stade de France after the attacks. Explosions were heard during the soccer match between France and Germany.

Spectators gather on the field of the Stade de France after the attacks. Explosions were heard during the soccer match between France and Germany.

A wounded man is evacuated from the Stade de France in Saint-Denis, outside Paris.

A wounded man is evacuated from the Stade de France in Saint-Denis, outside Paris.

Police secure the Stade de France in Saint-Denis, north of Paris, following explosions during the soccer match between France and Germany.

Police secure the Stade de France in Saint-Denis, north of Paris, following explosions during the soccer match between France and Germany.

A riot police officer stands by an ambulance near the Bataclan concert hall in central Paris.

A riot police officer stands by an ambulance near the Bataclan concert hall in central Paris.

A woman walks past police and firefighters in the Oberkampf area of Paris.

A woman walks past police and firefighters in the Oberkampf area of Paris.

A medic tends to a wounded man following the attacks near the Boulevard des Filles du Calvaire.

A medic tends to a wounded man following the attacks near the Boulevard des Filles du Calvaire.

Wounded people are evacuated outside the scene of a hostage situation at the Bataclan theater in Paris on November 13.

Wounded people are evacuated outside the scene of a hostage situation at the Bataclan theater in Paris on November 13.

Rescuers evacuate an injured person on Boulevard des Filles du Calvaire, close to the Bataclan concert hall in central Paris.

Rescuers evacuate an injured person on Boulevard des Filles du Calvaire, close to the Bataclan concert hall in central Paris.

A body, covered by a sheet, is seen on the sidewalk outside the Bataclan theater.

A body, covered by a sheet, is seen on the sidewalk outside the Bataclan theater.

Spectators embrace each other as they stand on the playing field of the Stade de France stadium at the end of a soccer match between France and Germany in Saint-Denis, outside Paris, on November 13.

Spectators embrace each other as they stand on the playing field of the Stade de France stadium at the end of a soccer match between France and Germany in Saint-Denis, outside Paris, on November 13.

Spectators invade the pitch of the Stade de France stadium after the international friendly soccer match between France and Germany in Saint-Denis.

Spectators invade the pitch of the Stade de France stadium after the international friendly soccer match between France and Germany in Saint-Denis.

A survivor of the terrorist attack in the Bataclan is assisted following terror attacks, November 13. The violence at the Bataclan, which involved a hostage-taking, resulted in the highest number of casualties of all the attacks.

A survivor of the terrorist attack in the Bataclan is assisted following terror attacks, November 13. The violence at the Bataclan, which involved a hostage-taking, resulted in the highest number of casualties of all the attacks.

Rescuers evacuate an injured person near the Stade de France, one of several sites of attacks November 13 in Paris. Thousands of fans were watching a soccer match between France and Germany when the attacks occurred.

Rescuers evacuate an injured person near the Stade de France, one of several sites of attacks November 13 in Paris. Thousands of fans were watching a soccer match between France and Germany when the attacks occurred.

Forensics are working in the street of Paris after the terrorist attack on Friday, November 13. The words "horror," "massacre" and "war" peppered the front pages of the country's newspapers, conveying the shell-shocked mood.

Forensics are working in the street of Paris after the terrorist attack on Friday, November 13. The words "horror," "massacre" and "war" peppered the front pages of the country's newspapers, conveying the shell-shocked mood.

A woman is evacuated from the Bataclan theater early on November 14.

A woman is evacuated from the Bataclan theater early on November 14.

Victims of the shooting at the Bataclan concert venue in central Paris are evacuated to receive medical treatment on November 14.

Victims of the shooting at the Bataclan concert venue in central Paris are evacuated to receive medical treatment on November 14.

Police officers patrol the area around Notre Dame cathedral in Paris on November 14.

Police officers patrol the area around Notre Dame cathedral in Paris on November 14.

A man with blood on his shirt talks on the phone on November 14. He is next to the Bataclan theater, where gunmen shot concertgoers and held hostages until police raided the building.

A man with blood on his shirt talks on the phone on November 14. He is next to the Bataclan theater, where gunmen shot concertgoers and held hostages until police raided the building.

Police, firefighters and rescue workers secure the area near the Bataclan concert hall on November 14.

Police, firefighters and rescue workers secure the area near the Bataclan concert hall on November 14.

Medics evacuate an injured woman on Boulevard des Filles du Calvaire near the Bataclan early on November 14.

Medics evacuate an injured woman on Boulevard des Filles du Calvaire near the Bataclan early on November 14.

Security forces evacuate people on Rue Oberkampf near the Bataclan concert hall early on November 14.

Security forces evacuate people on Rue Oberkampf near the Bataclan concert hall early on November 14.

Shoes and a bloody shirt lie outside the Bataclan concert hall on November 14. Most of the fatalities occurred at the Bataclan in central Paris.

Shoes and a bloody shirt lie outside the Bataclan concert hall on November 14. Most of the fatalities occurred at the Bataclan in central Paris.

Forensic police search for evidence inside the Comptoir Voltaire cafe after the attacks.

Forensic police search for evidence inside the Comptoir Voltaire cafe after the attacks.

Police are out in force November 14 near La Belle Equipe, one of the sites of the terror attacks.

Police are out in force November 14 near La Belle Equipe, one of the sites of the terror attacks.

A forensic scientist works near a Paris cafe on Saturday, November 14, following a series of coordinated attacks in Paris the night before that killed scores of people. ISIS has claimed responsibility.

A forensic scientist works near a Paris cafe on Saturday, November 14, following a series of coordinated attacks in Paris the night before that killed scores of people. ISIS has claimed responsibility.

Some leaders say they either oppose taking in any Syrian refugees being relocated as part of a national program or asked that they be particularly scrutinized as potential security threats.

Only 1,500 Syrian refugees have been accepted into the United States since 2011, but the Obama administration announced in September that 10,000 Syrians will be allowed entry next year.

The Council on American-Islamic Relations said Monday, "Defeating ISIS involves projecting American ideals to the world. Governors who reject those fleeing war and persecution abandon our ideals and instead project our fears to the world."

Authority over admitting refugees to the country, though, rests with the federal government -- not with the states -- though individual states can make the acceptance process much more difficult, experts said.

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American University law professor Stephen I. Vladeck put it this way: "Legally, states have no authority to do anything because the question of who should be allowed in this country is one that the Constitution commits to the federal government." But Vladeck noted that without the state's participation, the federal government would have a much more arduous task.

"So a state can't say it is legally objecting, but it can refuse to cooperate, which makes thing much more difficult."

Kevin Appleby, director of migration policy at the U.S. Conference of Catholic Bishops, said one tactic states could use would be to cut their own funding in areas such as resettling refugees. The conference is the largest refugee resettlement organization in the country.

But "when push comes to shove, the federal government has both the plenary power and the power of the 1980 Refugee Act to place refugees anywhere in the country," Appleby said.

More than 250,000 people have died since the violence broke out in Syria in 2011, and at least 11 million people in the country of 22 million have fled their homes. Syrians are now the world's largest refugee population, according to the United Nations. Most are struggling to find safe haven in Europe.

Photos: Increased security following Paris attacks Photos: Increased security following Paris attacks People go through a security checkpoint to attend a Mass in homage to victims of the Paris terror attacks at Notre Dame cathedral in Paris on Sunday, November 15. French President Francois Hollande declared a state of emergency after the attacks in Paris on Friday, November 13, and said border security has been ramped up. The terrorist group ISIS claimed responsibility for the attacks. Hide Caption 1 of 13 Photos: Increased security following Paris attacks French Prime Minister Manuel Valls, center, speaks with police forces with French Interior minister Bernard Cazeneuve, left, and Defence Minister Jean-Yves Le Drian at the Gare du Nord railway station in Paris on November 15 about security measures after the attacks. Hide Caption 2 of 13 Photos: Increased security following Paris attacks French police secure the perimeter after panic broke out among mourners who paid their respects at the attack sites at restaurant Le Petit Cambodge and the Carillon Hotel in Paris on November 15. Hide Caption 3 of 13 Photos: Increased security following Paris attacks Mounted police officers patrol in front of the Eiffel Tower in Paris on November 15. Hide Caption 4 of 13 Photos: Increased security following Paris attacks Security personnel inspect vehicles at the border between Belgium and France on Saturday, November 14. Hide Caption 5 of 13 Photos: Increased security following Paris attacks A police officer stands guard outside the Cafe Bonne Biere in the Rue de la Fontaine au Roi in Paris on November 14. Hide Caption 6 of 13 Photos: Increased security following Paris attacks A French police officer guards the French-Italian border on November 14 in Menton, France. Hide Caption 7 of 13 Photos: Increased security following Paris attacks Soldiers from the 3rd Marine Infantry Parachute Regiment of Carcassonne arrive at Charles de Gaulle Airport in Paris as security reinforcements on November 14. Hide Caption 8 of 13 Photos: Increased security following Paris attacks Soldiers patrol the Eiffel Tower on November 14. Hide Caption 9 of 13 Photos: Increased security following Paris attacks French police check vehicles on the bridge between Strasbourg and Kehl, Germany, on November 14. Hide Caption 10 of 13 Photos: Increased security following Paris attacks Police vehicles are parked near the entrance to the Louvre in Paris on November 14. Interior Minister Bernard Cazeneuve said the state of emergency in France could mean restrictions on people's movements. Airports in France remained open, and airlines were still flying there, though some airlines reported canceled flights. Hide Caption 11 of 13 Photos: Increased security following Paris attacks French police check vehicles on the so-called European bridge between Strasbourg and Kehl, Germany, on November 14. Hide Caption 12 of 13 Photos: Increased security following Paris attacks Police stand guard at a train station in Paris on November 14. Hide Caption 13 of 13

In announcing that his state would not accept any Syrian refugees, Texas Gov. Greg Abbott tweeted Monday on his personal account, "I demand the U.S. act similarly," he said. "Security comes first."

BREAKING: Texas will not accept any Syrian refugees & I demand the U.S. act similarly. Security comes first. https://t.co/uE34eluXYd — Greg Abbott (@GregAbbott_TX) November 16, 2015

In a letter to President Barack Obama, Abbott said "American humanitarian compassion could be exploited to expose Americans to similar deadly danger," referring to Friday's deadly attacks in Paris.

In a statement from Georgia's governor, Republican Nathan Deal, he said Georgia will not accept Syrian refugees "until the federal government and Congress conducts a thorough review of current screening procedures and background checks."

I've issued an executive order directing state agency heads to prevent the resettlement of Syrian refugees in GA. https://t.co/4b41tsIYcm — Governor Nathan Deal (@GovernorDeal) November 16, 2015

Alabama Gov. Robert Bentley also rejected the possibility of allowing Syrian refugees into his state and connected refugees with potential terror threats.

"After full consideration of this weekend's attacks of terror on innocent citizens in Paris, I will oppose any attempt to relocate Syrian refugees to Alabama through the U.S. Refugee Admissions Program," Bentley said Sunday in a statement.

"As your governor, I will not stand complicit to a policy that places the citizens of Alabama in harm's way."

I will not stand complicit to a policy that places the citizens of Alabama in harm's way. We refuse Syrian refugees. https://t.co/HTpflJUiPc — Gov. Robert Bentley (@GovernorBentley) November 16, 2015

There is currently no credible threat against the state, the governor's office said, and no Syrian refugees have been relocated to Alabama so far.

As the list of states blocking refugees grows, at least one state, Delaware, announced that it plans to accept refugees.

"It is unfortunate that anyone would use the tragic events in Paris to send a message that we do not understand the plight of these refugees, ignoring the fact that the people we are talking about are fleeing the perpetrators of terror," Gov. Jack Markell said in a statement.

States whose governors oppose Syrian refugees coming in:

-- Alabama

-- Arizona

-- Arkansas

-- Florida

-- Georgia

-- Idaho

-- Illinois

-- Indiana

-- Iowa

-- Kansas

-- Louisiana

-- Maine

-- Maryland

-- Massachusetts

-- Michigan

-- Mississippi

-- Nebraska

-- Nevada

-- New Hampshire

-- New Jersey

-- New Mexico

-- North Carolina

-- North Dakota

-- Ohio

-- Oklahoma

-- South Carolina

-- South Dakota

-- Tennessee

-- Texas

-- Wisconsin

-- Wyoming

States whose governors say they will accept refugees:

-- Colorado

-- Connecticut

-- Delaware

-- Hawaii

-- Pennsylvania

-- Vermont

-- Washington

Michigan Gov. Rick Snyder said the state would "put on hold our efforts to accept new refugees."

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"Michigan is a welcoming state and we are proud of our rich history of immigration. But our first priority is protecting the safety of our residents," he said in a statement.

Snyder demanded that the Department of Homeland Security review its security procedures for vetting refugees but avoided blanket suspicion of people from any region.

"It's also important to remember that these attacks are the efforts of extremists and do not reflect the peaceful ways of people of Middle Eastern descent here and around the world," Snyder said.

And Arkansas Gov. Asa Hutchinson posted on his official Twitter account that he would "oppose Syrian refugees being relocated to Arkansas."

As Governor I will oppose Syrian refugees being relocated to Arkansas. — Gov. Asa Hutchinson (@AsaHutchinson) November 16, 2015

Mississippi, Ohio bristle at taking refugees

The governors of Ohio and Mississippi announced their states would not allow Syrian refugees.

Jim Lynch, a spokesman for Ohio Gov. John Kasich , issued this statement:

"The governor doesn't believe the U.S. should accept additional Syrian refugees because security and safety issues cannot be adequately addressed. The governor is writing to the President to ask him to stop, and to ask him to stop resettling them in Ohio. We are also looking at what additional steps Ohio can take to stop resettlement of these refugees."

Kasich is a Republican presidential candidate.

Mississippi Gov. Phil Bryant wrote on Facebook that he was working with the state's homeland security department to "determine the current status of any Syrian refugees that may be brought to our state in the near future.

"I will do everything humanly possible to stop any plans from the Obama administration to put Syrian refugees in Mississippi. The policy of bringing these individuals into the country is not only misguided, it is extremely dangerous. I'll be notifying President Obama of my decision today to resist this potential action."

Louisiana: 'Kept in the dark'

Louisiana governor and GOP presidential candidate Bobby Jindal complained bitterly in an open letter to Obama that the federal government had not informed his government about refugees being relocated to his state last week.

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"It is irresponsible and severely disconcerting to place individuals, who may have ties to ISIS, in a state without the state's knowledge or involvement," Jindal said in his letter Saturday.

He demanded to know more about the people being placed in Louisiana to avoid a repeat of the Paris attacks and wanted to know whether screening would be intensified for refugees holding Syrian passports.

And he suggested Obama hold off on taking in more refugees.

"It would be prudent to pause the process of refugees coming to the United States. Authorities need to investigate what happened in Europe before this problem comes to the United States," Jindal said.

Republican candidate Donald Trump called accepting Syrian refugees "insane."

"We all have heart and we all want people taken care of, but with the problems our country has, to take in 250,000 -- some of whom are going to have problems, big problems -- is just insane. We have to be insane. Terrible," Donald Trump said at a rally in Beaumont, Texas.

It's not clear why Trump used the 250,000 figure.

The Obama administration has previously announced plans to take in 10,000 Syrian refugees next year.

While addressing reporters on Monday, Obama called out Republican candidates who have objected to admitting refugees to the United States.

"When I hear a political leader suggesting that there should be a religious test for which a person who is fleeing from a war torn country is admitted... when some of those folks themselves come from families who benefited from protection when they were fleeing political persecution, that is shameful," the President said. "We don't have religious tests to our compassion."

New York: 'Virtually no vetting'

A senior White House security official attempted to allay concerns about the vetting of Syrian refugees.

Photos: Refugees wait for a boat to a new life Photos: Refugees wait for a boat to a new life Tens of thousands of migrants have arrived on the Greek island of Lesbos in recent months. In early November a CNN team met little Meryem, who was hit by shrapnel from a barrel bomb in the Idlib province of Syria. The piece of shrapnel very nearly struck her heart, says her mother Amroon who was also hit in the same attack. It tore through her left hand, leaving it with little range of movement. Hide Caption 1 of 5 Photos: Refugees wait for a boat to a new life Farah (R), 10, is from Baghdad. She has been waiting with her younger brother and parents for a boat to Athens for two days. When asked why they are leaving, she says, "the situation in Baghdad is not good, that's what daddy said." Hide Caption 2 of 5 Photos: Refugees wait for a boat to a new life Ali is 15 months old. He's also waiting to get on a boat to Athens. His hometown of Jarablus in northern Syria is an ISIS stronghold. His uncle, who he never got to meet, was one of the first five people beheaded for attempting to resist ISIS in Jarablus. Hide Caption 3 of 5 Photos: Refugees wait for a boat to a new life Emine and Wahibe, aged 2.5 and 4, respectively, are sisters from Aleppo, Syria. They are waiting with their parents for the boat to take them to Athens. Hide Caption 4 of 5 Photos: Refugees wait for a boat to a new life Confiscated boat motors at the customs area in Lesbos. Officers there say this is just a tiny fraction of the motors they have impounded from refugee dinghies coming to the island from Turkey. Hide Caption 5 of 5

On NBC's "Meet the Press" Sunday, White House Deputy National Security Adviser Ben Rhodes said, "We have very extensive screening procedures for all Syrian refugees who have come to the United States. There is a very careful vetting process that includes our intelligence community, our National Counter Terrorism Center, the Department of Homeland Security, so we can make sure that we are carefully screening anybody that comes to the United States."

New York Rep. Peter King, speaking on Fox News, cast doubt on Rhodes' comments.

"What he said about the vetting of the refugees is untrue. There is virtually no vetting cause there are no databases in Syria, there are no government records. We don't know who these people are."

On Sunday, investigators said that one of the Paris bombers carried Syrian identification papers -- possibly forged -- and the fear of Syrian refugees grew worse.