The dinner was a follow-up to a meeting that Mr. Schumer and Ms. Pelosi had with the president in the Oval Office last week, during which Mr. Trump agreed to the Democrats’ proposal for a vote on a debt-ceiling increase and a government funding measure that also included a Hurricane Harvey aid package.

While the two top Republican congressional leaders, Senator Mitch McConnell and Speaker Paul D. Ryan, attended that meeting, they were absent from the Wednesday night dinner.

A total of 11 people were seated at the table in the Blue Room of the White House on Wednesday night, with the first 30 minutes of the meeting focused on China trade issues, according to one person briefed on the dinner. The meal served was Chinese food, an intentional nod to China trade, on which Mr. Trump and Mr. Schumer hold their closest views.

On the DACA program, Mr. Trump has given Congress six months to find a legislative solution to extend the protections that President Barack Obama granted by executive order. But before the dinner on Wednesday night, prospects for quickly enacting a replacement for DACA had appeared to be flagging in Congress.

“With all the other things going on right now, it’s kind of put on the back burner,” said Representative Mike Coffman, Republican of Colorado, who had pulled back a petition he had hoped to use to force the House to take up legislation on the program. Representative Bob Goodlatte of Virginia, chairman of the House Judiciary Committee, has said that the program is at the end of a list of immigration priorities.

Several top Republican leaders in Congress, including Mr. Ryan, have said that they want to tackle the issue of the young immigrants in conjunction with a broader immigration reform and border security effort.

But Republicans have been mostly enraged with Mr. Trump since the Oval Office meeting last week, where he sided with the Democratic leadership over his own party and his own Treasury secretary in favor of a December debt-ceiling vote. Mr. Ryan, who preferred a longer-term deal, had called such a three-month plan ridiculous.