US President Donald Trump and top Democratic leaders agreed to work out an agreement that would protect the nation's "Dreamers" from deportation and enact border security measures that don't include building a physical wall, according to people familiar with the meeting.

The President discussed the deal during a dinner at the White House with Senate Minority Leader Charles Schumer and House Minority Leader Nancy Pelosi. The meal included Chinese food and chocolate pie.

In a statement, the White House described the meeting as "constructive" and that it focused on "tax reform, border security, DACA, infrastructure and trade".

"The Administration looks forward to continuing these conversations with leadership on both sides of the aisle," the statement added.

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But aides familiar with the exchange said that Trump and the party leaders agreed to move quickly on legislation to protect the roughly 690,000 people protected under the Deferred Action for Childhood Arrivals, or DACA, programme that is set to expire in June.

In a statement, Schumer and Pelosi said they had "a very productive meeting at the White House with the President. The discussion focused on DACA. We agreed to enshrine the protections of DACA into law quickly, and to work out a package of border security, excluding the wall, that's acceptable to both sides".

They said the dinner also focused on ensuring that the Administration works to shore up the Affordable Care Act in the coming weeks.

Earlier, Trump had told a bipartisan group of House lawmakers during a White House meeting that he wants to resolve the DACA issue "real soon," according to Congressman Henry Cuellar, (D), who attended.

Cuellar said that he told Trump the Dream Act has sufficient bipartisan support to pass and that the White House should be pushing for a vote.

Trump, Cuellar said, told the group: "Oh, it will be on the floor".

Even if the President and Democratic leaders claim to cut a deal, it will need the support of GOP leaders, who are already wary of the spending agreement Trump brokered with them last week.

Pelosi and House Speaker Paul Ryan, met earlier today to begin discussing the broad parameters of the forthcoming immigration debate. Ryan's team signalled that despite the Administration's eagerness to quickly seal the deal, it will take awhile.

AshLee Strong, Ryan's spokeswoman, said that regarding the plight of the dreamers, the speaker "reiterated that any solution needs to address border security and enforcement, which are the root causes of the problem. Discussions among the Republican conference will continue in the coming weeks".