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."
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."
The president says that justice needs to be swifter and stronger for terrorists.