Phoenix, Arizona (CNN) -- Arizona Gov. Jan Brewer signed a bill Friday that requires police in her state to determine whether a person is in the United States legally, which critics say will foster racial profiling but supporters say will crack down on illegal immigration.

The bill requires immigrants to carry their alien registration documents at all times and requires police to question people if there is reason to suspect that they're in the United States illegally. It also targets those who hire illegal immigrant day laborers or knowingly transport them.

The Republican governor also issued an executive order that requires additional training for local officers on how to implement the law without engaging in racial profiling or discrimination.

"This training will include what does and does not constitute reasonable suspicion that a person is not legally present in the United States," Brewer said after signing the bill.

"Racial profiling is illegal. It is illegal in America, and it's certainly illegal in Arizona," Brewer said.

The rules, to be established in by the Arizona Peace Officers Standards and Training Board, are due back to her in May. The law goes into effect 90 days after the close of the legislative session, which has not been determined.

What will Arizona's immigration law do?

Previously, officers could check someone's immigration status only if that person was suspected in another crime.

Brewer's executive order was in response to critics who argue that the new law will lead to racial profiling, saying that most police officers don't have enough training to look past race while investigating a person's legal status.

"As committed as I am to protecting our state from crime associated with illegal immigration, I am equally committed to holding law enforcement accountable should this stature ever be misused to violate an individual's rights," Brewer said.

She added that the law would probably be challenged in courts and that there are those outside Arizona who have an interest in seeing the state fail with the new measure.

"We cannot give them that chance. We must use this new tool wisely and fight for our safety with the honor Arizona deserves."

The bill is considered to be among the toughest immigration measures in the nation. Supporters say the measure is needed to fill a void left by the federal government's failure to enforce its immigration laws.

Read the full text of Arizona Senate Bill 1070 (PDF)

Its leading sponsor, state Sen. Russell Pearce, said this week, "Illegal is not a race; it's a crime."

"We're going to take the handcuffs off of law enforcement. We're going to put them on the bad guy," said Pearce, a Republican.

Fellow Republican state Sen. Frank Antenori said the biggest reason he supported the bill was because a rancher in one of the counties he represents was murdered by someone who crossed the U.S. border with Mexico illegally. He said the person of interest in the killing had crossed the border numerous times and cited other similar violent crimes.

"The citizens of this state are tired of the catch and release that is going on by the federal government where they grab people, they process them, and they take them back and drop them on the other side of the border," Antenori said. "They just come back, and we have no border security down here."

After the signing, the Arizona Association of Chiefs of Police, which had opposed the measure, issued a statement saying, "law enforcement professionals in the State of Arizona will enforce the provisions of the new law to the best of their abilities."

The state's largest police union, the Arizona Police Association, is in favor of the law.

In the hours leading up to the bill's signing, about 2,000 people rallied at the Arizona capital, and President Barack Obama, in the nation's capital, called the legislation "misguided" but said the federal government must act on the immigration issue.

Read excerpts from remarks Friday by Obama and Brewer

"Our failure to act responsible at the federal level will only open the door to irresponsibility by others. That includes, for example, the recent efforts in Arizona, which threaten to undermine basic notions of fairness that we cherish as Americans, as well as the trust between police and their communities that is so crucial to keeping us safe," the president said at a naturalization ceremony for 24 members of the military.

Brewer's counterpart in neighboring New Mexico, Gov. Bill Richardson, called the new law "a terrible piece of legislation."

"It's against the democratic ideals of this country," he told CNN's "Situation Room." "It's a step backwards. It's impractical."

He said the law would not combat the problem of illegal immigration or take the place of comprehensive reform.

iReport: Share your thoughts on immigration policy

Latino members of Congress also slammed the bill.

"When you institutionalize a law like this one, you are targeting and discriminating at a wholesale level against a group of people," Rep. Raul Grijalva, D-Arizona, said Tuesday.

Grijalva closed his two district offices Friday when an unidentified caller threatened to blow up his Tucson office and kill his staff members. The caller also said he was going to be "exercising my civil liberties, and I'm shooting Mexicans at the border," according to Grijalva's district director, Ruben Reyes, who fielded one of the calls.

Grijalva and Rep. Luis Gutierrez, chairman of the Congressional Hispanic Caucus Task Force on Immigration Reform, had called on Brewer to veto the measure.

Gutierrez is a leading supporter of a proposed overhaul of U.S. immigration laws and said the Arizona issue shows why an overhaul is necessary. He has urged Obama to "put his back into the push" and to let Arizona know that federal law trumps state legislation on immigration.

Challenges expected - Coverage from CNN affiliate KPHO

The Virginia-based Hispanic Leadership Fund also criticized the law, saying in a written statement, "Having to 'carry your papers' is a hallmark of authoritarian regimes -- not of the Constitutional Republic that our Founding Fathers wisely passed on to us. Arizonans and all Americans deserve an immigration system that works, not a draconian big government desecration of the Bill of Rights."

Brewer said that "decades of federal inaction and misguided policies" have created "a dangerous and unacceptable situation."

The governor said Arizona's law mirrors federal statutes on immigration enforcement, "despite the erroneous and misleading statements suggesting otherwise."

Asked what criteria will be used to establish reasonable suspicion of someone's legal status, Brewer said, "I don't know. I do not know what an illegal immigrant looks like."

However, she added, her executive order requires the Arizona Peace Officers Standards and Training Board to address the issue.

"I know that if AZPOST gets [itself] together, works on this law, puts down the description, that the law will be enforced civilly, fairly and without discriminatory points to it."