WASHINGTON—President Trump said Thursday that the White House and congressional negotiators were no closer to an immigration deal, five days after he agreed to end the partial government shutdown, and reiterated he is willing to act alone to build a wall on the southern border.

“I’m not waiting for this committee,” Mr. Trump said, referring to a bipartisan group of legislators from the House and Senate who are working to hash out an agreement that would prevent another shutdown Feb 15.

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