By Tal Kopan, CNN

(CNN) -- President Donald Trump gave some key Republicans insight into his thinking on immigration at a White House dinner on Monday night -- assuring them a similar dinner with Congress' top Democrats had not resulted in a deal.

The conversation included what to do to replace the Obama-era Deferred Action for Childhood Arrivals program, which protects young undocumented immigrants brought to the US as children from deportation, now that Trump has announced an end to the program.

Trump, attendees said, remains focused on finding a solution while also emphasizing border security. But it was unclear whether Trump's border wall would have to be a part of any DACA deal

At the dinner was House Majority Leader Kevin McCarthy, House Judiciary Committee Chairman Bob Goodlatte, Senate Majority Whip John Cornyn, Arkansas Sen. Tom Cotton and Georgia Sen. David Perdue, according to the White House. Cornyn has introduced a $15 billion border security bill, Goodlatte has been a longtime proponent of tough immigration enforcement measures, and Cotton and Perdue have introduced legislation that Trump has endorsed that would halve and transform the US green card system.

Cornyn told reporters he got the sense that Trump is ultimately focused on reaching a deal and that he wasn't "fixed on any particular point of view."

Topics that came up included border security and the RAISE Act, which is Cotton and Perdue's bill to transform employment-based green cards into a merit system that heavily favors high-skilled, highly educated and English-speaking immigrants, according to Cornyn.

"I think those were all, sort of, in play," Cornyn told reporters on the Hill.

Perdue said that Trump seems interested in a deal, and that the conversation Monday night was about a "framework."

Trump "is still committed to trying to get a wall," Perdue said, but didn't say that it necessarily has to be part of this deal. "I mean, border security now is more than just a wall."

Cotton came away with a sense that Trump had insisted on some new requirements. The Arkansas Republican told Politico that Trump wanted to limit any deal to only current recipients of DACA, not just eligible immigrants, and that there must be limits to family members that could be sponsored to come to the US on top of that.

"The President was very clear: Any effort to codify DACA needs to, one, be limited to DACA, so the first criteria under the law should be, you have a DACA permit today," Cotton said. "Second, any deal has to end chain migration. And then third, it ought to include some kind of enhanced measures, whether it's on the border or interior enforcement or what have you."

A White House official described the dinner in broad strokes, saying the conversations would continue.

"The dinner focused on shared priorities for immigration legislation, including legal authorities to close border security loopholes, restoring interior enforcement, and reforming the legal immigration system," the official said on condition of anonymity. "In addition, they discussed other agenda items for the fall such as tax reform and disaster relief. The President looks forward to continuing these conversations with bipartisan members of Congress."

The dinner follows a meeting Trump had with Senate Minority Leader Chuck Schumer and House Minority Leader Nancy Pelosi last month, after which the Democrats felt that Trump had agreed on the whole to a deal that would include Democrats' preferred DACA legislation, the Dream Act, along with some border security measures. Trump insisted on Twitter afterward that no specific deal had been struck, but has spoken repeatedly about Congress needing to act before the end of the six-month window he has allowed before permits under the program begin expiring.

Reacting to the Republicans' dinner on Tuesday, Schumer said Trump should be clear and public if he's changing his mind on any immigration plan.

"We were explicit that the President would support the Durbin-Graham proposal, the Dream Act," Schumer said on Capitol Hill. "If they're backing off on that we ought to know. That was not said. ... If they're backing off of it because of pressure from the far right, America ought to know and we ought to know."

The-CNN-Wire™ & © 2017 Cable News Network, Inc., a Time Warner Company. All rights reserved.