Trump's strong statement came after the Islamic State terror group claimed that the attack on October 31 was carried out on its behalf by a domestically radicalised Uzbek immigrant to the US.
According to New York Times, the investigators found videos of ISIS fighters killing prisoners and also videos of how to make explosives.
Ultimately, Saipov sped down a bike path on a riverfront esplanade in a rented truck for almost a mile Tuesday, running down cyclists and pedestrians, before crashing into a school bus, authorities said.
Federal Bureau of Investigation officials said Saipov waived his Miranda rights and said he "felt good about what he had done", the complaint said. Prosecutors announced federal terrorism charges against Saipov late Wednesday, which means he can get the death penalty if convicted - even though NY state has no death penalty.
Sen. Lindsay Graham, a Republican, on Thursday repeated his criticism of the Justice Department for charging Saipov in the courts rather than treating him as an enemy combatant.
On Thursday, mourners gathered to hold a vigil for the victims of the attack that also left 13 people injured.
According to federal investigators, Saipov started planning the attack about a year ago and wanted to inflict maximum damage and chose Halloween as their will be more people out on the streets.
He's been charged with one count of providing material support to a terror organization and one count of violence and destruction of a motor vehicle resulting in death.
A police officer shot Saipov after he exited the truck brandishing paintball and pellet guns.
In the past few years, the Islamic State group has exhorted followers online to use vehicles, knives or other close-at-hand means of killing people in their home countries.
SHOULD GET DEATH PENALTY!' the President tweeted Wednesday night. He repeated the call Thursday, saying he'd love to send the "NYC terrorist" to Guantanamo, but that process would take longer than going through the federal system.
He also said the alleged killer should face the death penalty.
New York Governor Andrew Cuomo said Saipov had been radicalised after moving to the United States.
Miller said Saipov had never been the subject of a criminal investigation by the FBI or NY police, but appears to have links to people who have been investigated.
The New York Times reported that he was a university-educated accountant from a well-off family who won the green card lottery and moved to OH, with dreams of prospering, before eventually being forced to find work as a trucker.