WASHINGTON — The House on Tuesday failed to overturn President Trump’s first veto, leaving the declaration of a national emergency at the southwestern border intact despite the bipartisan passage of a resolution attempting to nullify the president’s circumvention of Congress to fund his border wall.

Despite concerns about the constitutional separation of powers and the effect of Mr. Trump’s move on local military projects, the 248-to-181 vote fell short of the two-thirds majority needed to kill the national emergency declaration.

Republicans in both chambers had joined Democrats in passing the resolution disapproving his national emergency just weeks ago, voicing discomfort over the president’s intent to divert funding to the construction of a border wall without congressional approval. Mr. Trump, issuing the first veto of his administration, had called the resolution “dangerous,” “reckless,” and a “vote against reality.”

But only 14 Republicans ultimately joined House Democrats in voting to override the veto, one more than the 13 who voted for the resolution of disapproval a month ago. (Representative John Katko, Republican of New York, had said he would support the measure, but missed the earlier vote.)