Schumer responded by accusing Trump of politicizing the attack, and added that the White House is also seeking to cut the federal counter-terrorism budget.
“I have always believed and continue to believe that immigration is good for America,"
Schumer said. "President Trump, instead of politicizing and dividing America, which he always seems to do at times of national tragedy, should be focusing on the real solution — anti-terrorism funding— which he proposed cutting in his most recent budget."
Schumer was a member of the House of Representatives in 1990 when the diversity visa program was created, and conservative media outlets have highlighted his role in drafting the legislation at the time.
Trump, who called for "extreme vetting" after the truck attack that left at least eight people dead, said in a follow-up tweet: "We are fighting hard for Merit Based immigration, no more Democrat Lottery Systems. We must get MUCH tougher (and smarter)."
In that message, Trump referenced the morning news program "Fox and Friends."
The suspect, Sayfullo Saipov, came to the United States from Uzbekistan, and media reports suggest he may have arrived through the diversity visa program.
Rep. Adam Schiff, D-Calif., the top Democrat on the House Intelligence committee criticized Trump's response Wednesday on MSNBC's Morning Joe:
"There are legitimate reasons to look at how much should we take immigration, new immigrants on the base of diversity, how much on the basis of merit," Schiff said. But "I’ve never really heard this made as a security argument. To use this tragedy in that way to push an agenda is not what the president ought to be doing right now."
Trump made immigration restrictions and "radical Islamic terrorism" major themes of his presidential campaign; Democrats accused him of using the terrorism issue to sow fear and crack down on immigration in general.