During his remarks, Trump commented on the terror attack in New York City.
He also pledged to end the green card lottery under which he said the man suspected of killing eight people in Manhattan on Tuesday entered the US. "Send him to Gitmo".
Since the September 11, 2001, terror attacks, no suspected terrorists detained on US soil have been sent to Guantánamo.
Trump quoted a guest who appeared on Fox and Friends Wednesday morning and said Schumer, who was born and raised in Brooklyn, was "importing Europe's problems".
The President described the suspect in custody, Sayfullo Habibullaevic Saipov, as an "animal", and hit out at the program Saipov reportedly used in 2010 to come to the United States, from Uzbekistan.
"We need quick justice and we need strong justice", he said.
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"We are so politically correct, we are afraid to do anything", Trump said. "What we have right now is a joke".
Sen. John McCain, R-Ariz., also called for trying Saipov at Guantanamo, according to the Huffington Post. Lindsey Graham, R-S.C., called on the president to treat the alleged attacker as an enemy combatant. Law-enforcement authorities said the suspect in NY followed an ISIS playbook to carry out the attack.
"We must not consider these attacks on our homeland in isolation, but rather recognize them for what they are: acts of war", he said.
McCain later clarified in a written statement that Saipov "should be held and interrogated-thoroughly, responsibly, and humanely-as an enemy combatant consistent with the Law of Armed Conflict".
Sen Lindsey Graham, Republican of SC, advocated treating him as an "enemy combatant", a designation that strips away due process protections like the right to challenge their imprisonment. "As soon as possible, the administration should notify Congress how it plans to proceed with the interrogation and trial of this suspect". (However, Schumer he was also a player in a 2013 immigration overhaul bill that would have eliminated the program).