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WASHINGTON — President Donald Trump said Wednesday he would "certainly consider" sending the man suspected of mowing down eight people and injuring others with a rented truck in New York City to the U.S. detention facility at Guantánamo Bay, Cuba.

"Send him to Gitmo — I would certainly consider that, yes," the president told reporters ahead of a Cabinet meeting at the White House.

Asked whether the alleged attacker's family could also represent a threat to the United States, Trump said he thought so.

"He did," the president said of Sayfullo Saipov, the Uzbek immigrant suspected of carrying out what law enforcement said was an Islamic State-inspired terrorist attack.

Late Wednesday, Trump tweeted that he supported capital punishment in the case.

NYC terrorist was happy as he asked to hang ISIS flag in his hospital room. He killed 8 people, badly injured 12. SHOULD GET DEATH PENALTY! — Donald J. Trump (@realDonaldTrump) November 2, 2017

Earlier, Sen. Lindsey Graham, R-S.C., argued that Saipov should be labeled an enemy combatant. That would allow the suspect to be interrogated without a lawyer present.

"If you take up arms against the United States in the name of radical Islam, you should be treated as a terrorist," Graham, a member of the Judiciary and Armed Services committees, said Wednesday. "You'll never convince me that the best way to gather intelligence in this war ... is reading them their Miranda rights."

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Later Wednesday, White House Press Secretary Sarah Huckabee Sanders said the president considers the suspect to be an enemy combatant.

As commander in chief, Trump can classify an individual as an enemy combatant, empowering the United States to detain that person without trial and without the rights granted to civilians, such as the right to a lawyer. The American Civil Liberties Union says more than half the detainees at Guantánamo Bay are being held without charge or trial.

Sen. John McCain, chairman of the Armed Services Committee, also argued for the designation.

"From Orlando to San Bernardino and Boston to Manhattan, we must not consider these attacks on our homeland in isolation, but rather recognize them for what they are: acts of war," McCain said in a statement. "As such, the New York terror suspect should be held and interrogated — thoroughly, responsibly, and humanely — as an enemy combatant consistent with the Law of Armed Conflict."

President Barack Obama's administration sought to stop using the enemy combatant term, arguing in court that it could detain certain terrorism suspects without it. But the Trump administration revived it, applying the designation to an American IS fighter captured Sept. 12 in Syria. As a candidate, Trump promised to "load up" Guantánamo Bay "with some really bad dudes."

However, an administration official told NBC News that there's likely no legal authority to send Saipov to the detention facility. Federal charges were filed Wednesday.

Carlton F.W. Larson, a professor at the University of California Davis law school whose specialties include enemy combatant designations, told NBC News that it's unlikely that Justice Department lawyers would support classifying Saipov as an enemy combatant when civilian courts can just as easily serve justice.

"If he doesn't die, he'll be tried in New York and most certainly be convicted," Larson said, "so I don't see a huge benefit to doing the enemy combatant thing, which would be legally troublesome and drag this thing out a lot more when you really just want to send this guy to jail."

But Trump argued Wednesday that the U.S. justice system takes too long.

"We also have to come up with punishment that's far quicker ... than the punishment these animals are getting right now," Trump said before the Cabinet meeting. "We need quick justice, and we need strong justice, much quicker and much stronger than we have right now, because what we have right now is a joke, and it's a laughing stock, and no wonder so much of this stuff takes place."

Graham told reporters that the suspect would not need to be held at Guantánamo — although he could be — and that it was possible that Saipov could later be reclassified as a civilian.

"The idea that America is not part of the battlefield is insane. Tell that to the people who were in the Twin Towers. Tell that to people in the Pentagon," Graham said in a reference to the terrorist attacks of Sept. 11, 2001. "The Constitution is not a suicide pact. We have a rule of law in place that covers situations like this. It's called the Law of War."

Despite a similar appeal from Graham in 2013, Obama did not declare Boston Marathon bomber Dzhokhar Tsarnaev an enemy combatant, but the Justice Department did invoke a public safety exception to delay reading the suspect his Miranda rights.

Tsarnaev, who was tried by a jury and sentenced to death in 2015, is on death row.

CORRECTION: (Nov. 2, 8:30 a.m.): An earlier version of this article misstated the day when President Trump tweeted in support of the death penalty. It was late Wednesday, not Thursday.

Ali Vitali reported from Washington, Jane C. Timm reported from New York.