US President Donald Trump has called for the green card lottery to be scrapped, saying it allowed the New York truck attack suspect into the US.
In a series of tweets he called for the immigration programme to be replaced with a merit-based system.
Mr Trump pinned blame for the scheme on Senator Chuck Schumer, who accused Mr Trump of cutting anti-terror funding.
Authorities have not yet confirmed how the suspect in Tuesday's attack, Sayfullo Saipov, immigrated to the US.
Mr Trump tweeted on Wednesday morning: "The terrorist came into our country through what is called the 'Diversity Visa Lottery Program,' a Chuck Schumer beauty. I want merit based.
He continued: "We must get MUCH tougher (and smarter)."
The US president also accused Senator Schumer, a New York Democrat, of "helping to import Europes [sic] problems".
"We will stop this craziness!" he added.
I guess it's not too soon to politicize a tragedy.— Chuck Schumer (@SenSchumer) November 1, 2017
What is the green card lottery?
The diversity visa lottery programme, also known as the green card lottery, grants permanent US residency every year to around 50,000 immigrants.
Mr Schumer did play a key role in crafting the legislation creating the lottery system in 1990.
It was passed in a cross-party vote and signed into law by a Republican President, George HW Bush.
But as Republican Senator Jeff Flake points out, Mr Schumer led a 2013 bipartisan immigration bill that proposed scrapping the green card lottery altogether.
The legislation would have transferred the permanent residency quota currently assigned to the green card lottery to immigrants with advanced skills.
The immigration bill passed the Senate but did not become law because it died in the House of Representatives.
What's Trump's immigration reform plan?
Mr Trump said in the aftermath of Tuesday's attack he was ordering the Department of Homeland Security "to step up our already Extreme Vetting Program", without elaborating.
The US leader said he wanted "extreme vetting" of immigrants during his presidential campaign last August.
As president, he introduced a ban on arrivals to the US from a number of mainly-Muslim countries - a move that has been challenged legally and is due before the Supreme Court in the coming weeks.
The American Civil Liberties Union civil rights group said the term extreme vetting was a "euphemism for discriminating against Muslims".
Mr Trump has also endorsed a bill by two Republican senators that would eliminate the lottery-based system.
The Reforming American Immigration for Strong Employment (Raise) Act was introduced in February, but has failed to attract the votes needed to pass the Senate.
It would also halve the number of legal immigrants to the US and cap the number of refugees.