President Donald Trump is calling the suspect in the New York City truck attack an "animal."
Trump says he will ask Congress to "immediately" begin work to terminate the Diversity Immigrant Visa Program, which he says was used by the alleged attacker to enter the United States.
Officials have not yet said that was the case.
Trump says "we will take all necessary steps to protect our people."
He also called for "quick justice" and "strong justice" for terror suspects in the wake of the attack, calling the current justice system a "joke."
"What we have right now is a joke and it is a laughing stock and no wonder so much of this stuff takes place," Trump told reporters.
Trump earlier in the day reiterated his desire to go to a merit-based immigration policy over the lottery program.
Speaking before a Cabinet meeting at the White House, Trump said "all of America is praying and grieving" with the victims. He says: "Our hearts break for them."
Further, the president said the alleged attacker, Sayfullo Saipov, brought in other people to the United States, and was the point of contact for 23 people, highlighting his desire to also do away with chain migration.
Trump also said he will consider sending the suspected truck attacker to the prison in Guantanamo Bay, Cuba, despite Saipov being an American citizen.
Responding to a shouted question from a reporter at a Cabinet meeting, Trump said, "I would certainly consider that. Send him to Gitmo."
Trump's comments come after Sen. Lindsey Graham, R-SC, called on the president to treat the alleged attacker as an enemy combatant. The suspect is currently in custody in New York City, but according to officials has not yet been formally charged.
Eight people died and at least 11 were seriously injured in the Tuesday attack.