WASHINGTON — President Trump said on Monday that he has rejected a proposal by Senator Lindsey Graham of South Carolina to temporarily reopen the government in an effort to jump-start talks with Democratic lawmakers on funding a border wall.

“I did reject it,” Mr. Trump said of the proposal, speaking to reporters as he boarded Marine One outside of the White House, en route to delivering a speech to a farm convention in New Orleans.

In an appearance on Fox News Sunday, Mr. Graham, a close ally of the president, pitched Mr. Trump on a plan for the president to agree to a vote by Congress to reopen the government for about three weeks “before he pulls the plug on the legislative option.” If there was no progress made during that time, Mr. Graham said, the president could then declare a national emergency as a way to obtain funding for a border wall without congressional action.