Authorities respond near a damaged school bus Tuesday Oct. 31 2017 in New York
"I know, I was there", Mr Flake, an outspoken critic of Trump, wrote on Twitter.
The suspect, Sayfullo Saipov, 29, who was hospitalised after a police officer shot and arrested him, ending Tuesday's rampage, confessed to authorities while in custody that he began planning the attack a year ago, according to the criminal complaint filed against him.
Mr Trump tweeted on Thursday that there is "also something appropriate" about keeping him "in the home of the terrible crime he committed".
NY does not have the death penalty and there has been no executions in the state since the 1960s.
Saipov's court appearance came just hours after President Donald Trump said he would consider sending Saipov to the Guantanamo Bay detention centre in Cuba - an idea the White House reinforced by saying it considered Saipov to be an "enemy combatant". He killed 8 people, severely injured 12.
"If your goal is to actually get justice for the victims, Guantanamo is a black hole, whereas the civilian courts are there, they're fast, their legitimacy is not regularly questioned", Vladeck said.
"It will endure." The phrase "it will endure" commonly refers to the Islamic State group, and Saipov had a cellphone loaded with the group's propaganda, an Federal Bureau of Investigation agent said in the criminal complaint.
In this courtroom drawing, defendant Sayfullo Saipov, right, addresses the court during his arraignment on federal terrorism charges, Wednesday, Nov. 1, 2017, at Manhattan Federal Court in NY. A 23-year-old New York City man, a 32-year-old New Jersey man, five Argentinians and a Belgian national were among the eight people who died. The Army sergeant's lawyers said candidate Trump's description of Bergdahl as a "dirty rotten traitor" who should be executed unfairly affected his trial.
Mr Schumer said. "The contrast between President Bush's actions after 9/11 and President Trump's actions this morning could not be starker".
On Wednesday, Trump vowed to "get rid" of the green card lottery "as soon as possible", seizing on the NY attack to press his campaign-agenda of restricting immigration.
"We don't think there's any way you could discredit the progress that has been made", Sanders said, contending that the attack reinforced the need to adopt the president's policies.
According to The Independent, his tweet calling for the NY terror attack suspect to be executed could potentially jeopardize the trial.
The attack was the deadliest in New York City since September 11, 2001, when suicide hijackers crashed two jetliners into the World Trade Center, killing more than 2,600 people.
The tweet could be argued as an attempt to influence a jury, but even without the intent, it still puts Trump at risk of being charged with contempt of court.
No one arrested in the United States has ever been sent to Guantanamo Bay, and the last time a person arrested overseas was sent there was in 2008.
Trump has passed on other chances to send suspects there, including earlier this week, when the Justice Department said a militant captured in Libya and accused of playing an instrumental role in the 2012 Benghazi attacks would be prosecuted in federal court in Washington, where a trial for the alleged mastermind is already under way.
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