The Trump White House said Tuesday that a lengthy bipartisan immigration meeting with lawmakers -- which played out in front of the cameras for nearly an hour -- has yielded a framework for future negotiation, covering everything from border security to Deferred Action for Childhood Arrivals (DACA).

“President Donald J. Trump just concluded a successful bipartisan and bicameral meeting on immigration reform,” White House Press Secretary Sarah Sanders said in a statement.

Sanders said participants reached “an agreement to negotiate legislation” that would tackle four key areas: border security, the diversity visa lottery, DACA and so-called “chain migration,” through which an immigrant's family members can enter the U.S. because their relative got in.

Still, later in the day, Trump said he would not budge on the border wall. “As I made very clear today, our country needs the security of the Wall on the Southern Border, which must be part of any DACA approval,” he tweeted.

Trump was clearly in a deal-making mood as he presided over the meeting, featuring Republican and Democratic lawmakers, that was replayed on television and showed him trying to reach common ground with both sides.

“There should be no reason for us not to get this done,” an enthusiastic Trump said.

Lawmakers and the White House still have much to discuss as they determine the specifics and scope of any agreement. Trump suggested during the meeting they might attack it in two phases.

The first step would be a deal to legislate the expiring DACA policy -- an Obama-era executive order that shielded some illegal immigrants who arrived in the country as children from deportation. A legislative fix for DACA would be coupled with an agreement on “border security,” which would appear to include Trump’s central campaign promise of a wall along the southern border.

The second step would be a much broader “comprehensive immigration reform” of the kind that lawmakers in both parties have unsuccessfully tried to work out for over a decade.

Moderate Republican lawmakers expressed delight at Trump’s apparent openness to negotiate, hoping that it could be the start of a deal that had eluded lawmakers for years.

“This was the most fascinating meeting I’ve been involved with in twenty plus years in politics,” Sen. Lindsey Graham, R-S.C., said in a statement after the meeting. “I very much appreciate President Trump’s attitude, demeanor, and desire to get something done that will make our nation more secure – while being fair to the Dreamers.”

He added, “President Trump has the right attitude. Now it is up to all of us in Congress to come up with a proposal that gets the job done.”

Democrats expressed cautious optimism about what they had seen during the meeting.

“I was encouraged about what the president said,” Senate Minority Leader Chuck Schumer, D-N.Y., told reporters. “The tone was very good. But the devil is in the details.”

“To the extent the meeting helped narrow the scope of our negotiations and prioritize the Dream Act, this was a positive first step,” Sen. Michael Bennet, D-Colo., said in a statement. “I'm pleased that there seemed to be an acknowledgement of the urgent need to pass this bipartisan bill immediately, so DACA recipients stop losing status and having their lives upended.”

Immigration hardliners, meanwhile, reacted with horror at Trump’s wheeling and dealing.

“Nothing Michael Wolff could say about @RealDonaldTrump has hurt him as much as the DACA lovefest right now,” tweeted commentator Ann Coulter, referring to Wolff’s tell-all book “Fire & Fury” from which gushed forth a torrent of negative headlines for the president last week.

Mark Krikorian, Executive Director of the Center for Immigration Studies, predicted that “if he ends up actually signing the kind of bill [Sen. Dick Durbin, D-Ill.] & co. want, GOP loses House & he's impeached (tho not necessarily removed) & out in 2020.”

In perhaps the most eyebrow-raising comment of the meeting, Trump said he wanted the first stage of negotiations to result in a “bill of love” -- reminiscent of former Florida Gov. Jeb Bush’s claim that illegal immigration can be an “act of love.” Bush was pilloried for that remark during the Republican presidential primary, in particular by Trump himself.

Bush tweeted that he was “encouraged [that] the President is seeking bipartisan solutions to our immigration challenges.”

“President Trump seemed to agree on a permanent solution for undocumented immigrant youth as the priority during today’s meeting, acknowledging that broader immigration reforms should be deferred to a phase two negotiation down the road. It’s now up to responsible lawmakers of both parties to reject further attempts by the nativist voices to derail policy negotiations with unfounded border alarmism and by adding unrelated, ideologically-driven poison pills to a narrowly-tailored deal,” American Civil Liberties Union director of immigration policy and campaigns Lorella Praeli responded.

Trump also took the sting out of the threat of a potential veto by promising to sign any deal that was hashed out by lawmakers and said that he would “take the heat” from conservatives opposed to such a comprehensive bill -- apparently acknowledging that he will hit opposition from his base.

“I will be signing it, I’m not going to say, oh gee, I want this or I want that. I’ll be signing it,” Trump said.

Yet, despite Trump’s apparent flexibility, some sticking points remained. Trump was asked whether there would be an agreement that did not include the border wall.

“No,” Trump responded.

Fox News’ Elizabeth Llorente, Chad Pergram and John Roberts contributed to this report.