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WASHINGTON — President Donald Trump pressed for action on immigration Thursday, saying the country's system has failed Americans and pressing for his wall on the southern border.

Any legislation to address the residency status of "Dreamers," currently in limbo, "must secure the border with a wall," the president said, flanked by Republican senators who came to the White House for a meeting on immigration.

"We’d love to take care of DACA, but we’re only going to do it under these conditions," he concluded, laying down a red line as Congress gears up for yet another round of fights to fund the government.

He also demanded that future legislation further restrict visa overstays and so-called chain migration, and end the visa lottery.

Among the issues complicating the funding battle to keep the government running is what to do about "Dreamers," which has remained an open question since the Justice Department announced last fall that it would end the Obama-era program that allowed young people who came to the United States illegally as children to remain in the country.

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Trump kicked the issue to Congress in September, while promising to "resolve the DACA issue with heart and compassion."

But actions to aid the young immigrants could upset Trump's base, who voted in support of the hard-line immigration policies he espoused during the campaign. Chief among those campaign promises was the wall, which Trump imagined at campaign rallies as "big" and "beautiful" — and maybe even branded with his name.

Democrats have already drawn their own red line, insisting that they will not accept any proposal that includes the construction of a border wall or any changes to legal immigration.

While Trump laid out his demands to television cameras ahead of the meeting with Republican senators, lawmakers have been asking for specifics from the White House on his demands, including how he defines a border wall, how much money he’d like in this deal and what specific changes he’d like to legal immigration. Senators who attended the meeting said the White House will release a paper with specific requests on Tuesday, the same day Trump will hold a bipartisan meeting on immigration, senators said.

Democrats are skeptical that the White House will release their specifics next week. It’s a promise they’ve been making for several weeks.

Meanwhile, a separate group of five bipartisan senators — Sens. Dick Durbin, D-Ill., Michael Bennett, D-Colo., Jeff Flake, R-Ariz., Cory Gardner, R-Colo., and Lindsey Graham, R-S.C. — are in the middle of their own negotiations revolving around both border security and the DREAM Act, legislation that provides a path to citizenship for the immigrants brought to the U.S. as children.

“We’re trying to get to a final working document. There’s a lot of working groups out there on this we got to get that to a single document,” said Sen. James Lankford, R-Okla., who attended the meeting with Trump.

Democrats want an agreement on DACA attached to any deal to fund the government for the remainder of the year, while Republicans say that any immigration deal should be separate. But Democrats say they will block any government funding deal unless immigration is addressed.

On Wednesday, senior administration officials met with House Speaker Paul Ryan, Senate Majority Leader Mitch McConnell, House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer to discuss potential paths forward for a budget agreement. DACA and the border were among the topics mentioned.

A joint statement from the White House, Ryan and McConnell issued after the meeting warned against "holding funding for our troops hostage for immigration policy."

Asked as she left the meeting if the group was getting anywhere, Pelosi told reporters, "I hope so."