While Mr. Esper did not detail which military construction initiatives would lose funding, he said in the letter that the money would not be taken from any family housing, barracks or dormitory projects.

Since Mr. Trump’s emergency declaration, the Defense Department had been examining an expansive $12.9 billion list of projects in nearly all 50 states and more than two dozen countries where American troops are stationed.

Department officials insisted on Tuesday that the military construction projects were only being delayed, not canceled. But regaining money for those projects will be up to Congress, which would have to approve new money to fund them, something that Democrats who control the House are loath to do.

“My view of it is that stealing money from military construction, at home and abroad, will undermine our national security, quality of life and morale of our troops, and that indeed makes America less safe,” Speaker Nancy Pelosi of California told members of her caucus on a private call on Tuesday, according to a Democratic official who spoke on the condition of anonymity to publicly discuss a private phone call.

Representative Debbie Wasserman Schultz, Democrat of Florida, who leads the House Appropriations subcommittee that oversees military construction, said on the same call that the committee would continue to resist replacing the diverted funds, according to the Democratic official.

“Every project that has been affected has gone through a rigorous multiyear review of the appropriateness and necessity of the construction process,” said Representative John Garamendi, Democrat of California, who oversees the House Armed Services Readiness Subcommittee. In an interview, he said he had not yet spoken with Mr. Esper, but warned “it will not be a pleasant conversation for him.”

Democrats on the Senate Appropriations Committee, in a letter to Mr. Esper on Tuesday night, demanded more information about how the decision was made and “why a border wall is more important to our national security and the well-being of our service members and their families than these projects.”

Several groups have challenged the Trump administration over the president’s efforts to divert funding for the wall. But in July, the Supreme Court gave Mr. Trump a victory in a separate but related case, overturning an appellate decision and ruling that the administration could tap money to proceed with wall construction while the matter proceeds. The court said the groups challenging the administration did not appear to have a legal right to do so, in an indication that the court’s conservative majority is likely to side with the administration in the end.