Mr. Trump was adamant in his demands for $5.6 billion in funding for a border wall, and he rejected Democrats’ proposals to fund the government while the two sides negotiated further. The Democrats refused to increase their offer of $1.3 billion for border security.

Mr. Trump asked congressional leaders to return to the White House on Friday to resume talks, an official said.

Go deeper: Nancy Pelosi is poised to reclaim the title of speaker of the House today. How she deals with Mr. Trump will define her tenure.

The Daily: In today’s episode, Senator Chuck Schumer discusses the shutdown and the era of divided government.