The White House labeled New York terrorist suspect Sayfullo Saipov as an enemy combatant Wednesday, with an angry President Trump saying he would consider sending the alleged Islamist who killed eight pedestrians with a truck to the notorious military prison at Guantanamo Bay.

White House press secretary Sarah Huckabee Sanders said the administration considers the 29-year-old Mr. Saipov, who emigrated to the U.S. from Uzbekistan, a fitting candidate for the military justice system in the war on terror.

“I believe we would consider this person to be an enemy combatant, yes,” she told reporters. “I think the actions that he took certainly justify that.”

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Justice Department spokesman Wyn Hornbuckle declined to comment Wednesday on whether there have been any discussions with the White House on sending Mr. Saipov to Guantanamo rather than filing criminal charges in a civilian court.

Federal authorities filed two criminal charges against Mr. Saipov Wednesday night in federal court, including providing material support for the Islamic State, but officials said the move doesn’t preclude the government declaring him an enemy combatant later.

“That’s a determination that will be made elsewhere,” said acting U.S. Attorney Joon Kim.

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“There can be federal charges in place and then someone can be declared an enemy combatant,” he said.

Some prominent lawmakers, such as Republican Sens. Lindsey Graham of South Carolina and John McCain of Arizona, are urging the administration to hold Mr. Saipov as an enemy combatant, a status that would give him fewer legal rights than in a civilian court, providing for him to be held in military custody.

“If you take up arms against the United States in the name of radical Islam, you should be treated as a terrorist,” said Mr. Graham, who has spent more than 30 years as a military lawyer.

After the charges were filed in federal court Wednesday night, Mr. Graham said the administration made “a huge mistake” by not immediately declaring Mr. Saipov an enemy combatant.

“It appears the Trump administration is continuing the Obama policy of criminalizing the war on terror,” Mr. Graham said. “It’s ridiculous to believe that one day of interviews in a hospital tells us all we need to know about Saipov’s terrorist ties. Now that he’s lawyered up, that will likely be the end of intelligence gathering except through plea bargaining.”

He said he’s “more concerned about intelligence gathering to help win a war. That is a process which takes time — time which is now lost.”

Mr. Kim said federal prosecutors brought the charges they can prove at this point, “and we intend to proceed with them.”

The fact a person is charged with a federal crime does not preclude designation as an enemy combatant, Mr. Kim said, commenting on past cases.

Investigators are turning up ample evidence showing that Mr. Saipov, who was shot and hospitalized after the attack, allegedly was motivated by Islamist extremism. Officials said he had been planning the attack for weeks and left a note in Arabic indicating his allegiance to the Islamic State.

New York Deputy Police Commissioner John Miller said Mr. Saipov’s attack followed the Islamic State’s playbook, saying the attack method has been used multiple times to kill hundreds in separate attacks in Europe.

At the White House, Mr. Trump addressed the first major Islamist attack in the U.S. of his presidency by calling for tougher immigration standards and harsher punishment for terror suspects.

“Send him to Gitmo,” Mr. Trump said of Mr. Saipov. “I would certainly consider that.”

The president added with obvious frustration, “We also have to come up with punishment that’s far quicker and far greater than the punishment these animals are getting right now. They’ll go through court for years and, at the end, who knows what happens.

“We need quick justice and we need strong justice, much quicker and much stronger than we have right now,” Mr. Trump said. “What we have right now is a joke and it’s a laughingstock. No wonder so much of this stuff takes place.”

Mrs. Sanders said the president “wasn’t necessarily advocating for” sending Mr. Saipov to Gitmo but speaking out of frustration that Washington isn’t taking firm enough steps to stop terrorist attacks.

“But he certainly would support [detention at Gitmo] if he felt like that was the best move,” she said.

Retired Gen. Charles Krulak, former Marine Corps commandant, was among those panning the suggestion.

“If the president truly wants ‘quick justice’ and ‘strong justice,’ he should never consider designating this suspect as an ‘enemy combatant’ or sending him to Guantanamo Bay,” Mr. Krulak said in a statement issued through Human Rights First. “Federal courts have a track record of fairly and expeditiously dealing with terrorism suspects, having handled more than six hundred cases since 9/11. The criminal justice process has enabled our government to gather timely, actionable intelligence to drive our counterterrorism efforts.”

Mr. Krulak said designating Mr. Saipov as an enemy combatant “does not make America safer.”

“On the contrary: It legitimizes individuals who are nothing more than thugs and criminals by branding them as the warriors they wish to be,” he said.

Anthony D. Romero, executor director of the American Civil Liberties Union, said sending Mr. Saipov to Guantanamo or treating him as an enemy combatant would “violate due process and the rule of law.”

“The FBI and our federal court system are more than capable of dealing with terrorism cases, and Guantanamo was shown long ago to be an epic failure,” Mr. Romero said.

The question about whether Mr. Saipov could be subject to military justice or tried in the civilian courts comes amid developments in several high-profile terrorism trials in the federal courts.

A federal jury last month convicted Ahmad Khan Rahimi, a 29-year-old New Jersey man, of planting two pressure-cooker bombs in New York City in 2016, one of which exploded and injured 30 people.

The federal trial of Ahmed Abu Khattala, the alleged mastermind behind the deadly 2012 attack on an American compound in Benghazi, Libya, got underway last month. Federal prosecutors are still presenting evidence in that case at the federal courthouse in Washington, D.C.

According to Justice Department documents from 2015, federal civilian criminal courts had convicted 620 people on terrorism-related charges since the Sept. 11, 2001, terrorist attacks.

The number of convictions has continued to climb. A Fordham University School of Law analysis found that from March 2014 through August 2017, 135 people had been charged with, and 77 people had been convicted of, crimes linked to the Islamic State.

Since 2001 military commissions have resulted in eight convictions, with four overturned. The five people accused of conspiring in the 9/11 attacks have yet to go to trial after more than a decade in custody at Guantanamo.

The Authorization for Use of Military Force approved by Congress after the 9/11 attacks allows the president to use force against those who “planned, authorized, committed, or aided” the terrorist attacks in 2001. The military has been relying on an expanded interpretation of the law to fight the Islamic State overseas, but it has not been applied to an Islamic State-affiliated suspect in the U.S.

⦁ Stephen Dinan contributed to this report.