Critics call it an unlawful program that promotes illegal immigration, lacked congressional approval and takes jobs from USA citizens.
He also said in the Thursday meeting he would prefer immigrants from countries like Norway instead.
Trump has said he favors stopping the diversity lottery, a system that reserves visas for people from countries that have relatively few immigrants in the United States.
Trump sought to focus the blame for any lack of progress on DACA on Democrats, tweeting: "DACA is probably dead because the Democrats don't really want it, they just want to talk and take desperately needed money away from our Military".
Efforts to extend the program are further complicated because it could make a funding bill to avert a government shutdown due Friday more hard.
Trump's decision to end DACA immediately became a talking point for congressional Democrats.
The sole Democratic participant in the Oval Office meeting, Senate Minority Whip Richard J. Durbin of IL, told reporters Friday that Trump had used the vulgar word "not just once but repeatedly" during the meeting.
The president also rejected as insufficient an immigration deal drafted by the bipartisan group of politicians who attended that meeting.
The president has said any deal must include funding for the wall as well as changes to make the immigration system a more merit-based structure.
The debate over Daca's fate came as politicians were forced to answer questions about whether Mr Trump is racist.
Republican Senator David Perdue, who was at the same White House meeting and had said he did not recall whether Trump made the comment, was more explicit Sunday.
Despite Trump's claims, Democrats have pushed to provide more funding for border security in exchange for the continuation of the DREAMERS Act.
"I'm telling you he did not use that word, George, " Perdue said, accusing Durbin of making a "gross misrepresentation" of what took place in the meeting: "It's not the first time Senator Durbin has done it, and it is not productive to solving the problem we're having".
One of Trump's top advisers, Homeland Security Secretary Kirstjen Nielsen, said on "Fox News Sunday" she did not recall if Trump used "that specific phrase". "I think that would show real leadership", she said on CNN's "State of the Union" on Sunday.
According to the reports, Judge Alsup, in his order on Tuesday, stated that the Trump administration's move to rescind DACA was done without following the proper legal procedures and that the federal government would have to "maintain the DACA program on a nationwide basis".
In another tweet Sunday, Trump said he wants people coming to the country "based on merit".
Perdue said that "the potential is there" for a deal to protect the "Dreamers" but that Democrats needed to get serious.