Trump had scrapped the Deferred Action for Childhood Arrivals (DACA) programme earlier this month which protect some 800,000 people who came to the US illegally as children.
The measures also provide temporary permits for work and study.
Trump had said he would cancel the scheme, while giving Congress six months to enact a replacement plan for DACA recipients.
Following talks over dinner at the White House, House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer said: "We agreed to enshrine the protections of DACA into law quickly, and to work out a package of border security, excluding the wall (Mexican), that's acceptable to both sides."
While Democratic leaders sought to declare the deal as a victory for their priorities, Republican votes will be needed for any immigration overhaul.
The White House, however, pushed back on the account of the agreement provided by the Democratic leaders.
"While DACA and border security were both discussed, excluding the wall was certainly not agreed to," White House Press Secretary Sarah Sanders said.
Trump wants to build a wall along the United States' border with Mexico to keep out illegal immigrants.
"These topics included tax reform, border security, DACA, infrastructure and trade. This is a positive step toward the President's strong commitment to bipartisan solutions for the issues most important to all Americans," the official said.
"The Administration looks forward to continuing these conversations with leadership on both sides of the aisle," said the White House official.
According to South Asian Americans Living Together (SAALT), a non-profit organisation, over 27,000 Asian Americans, including 5,500 Indians and Pakistanis, have already received DACA.
With the termination of DACA, as announced by the Trump administration, these individuals could face deportation at the discretion of the administration, it said.
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