WASHINGTON—President Donald Trump is open to waiting until later this year to secure funding for a wall along the border with Mexico, White House officials said Monday night, in a shift that could clear the way for lawmakers to strike a deal to avoid a government shutdown on Saturday.

Mr. Trump and top administration officials previously indicated the president wanted to include money to begin building a wall along the southern border in the bill to keep the government running after its current funding expires at 12:01 a.m....