WASHINGTON — The Pentagon plans to divert $3.8 billion intended for military equipment to the construction of a wall at the southwestern border, it informed lawmakers on Thursday, drawing bipartisan outrage and reviving a long-running battle with Congress over funding for President Trump’s signature campaign promise.

The formal notification to Congress on Thursday, which was obtained by The New York Times, was the latest bid by Mr. Trump’s administration to circumvent congressional control of federal spending and unilaterally seize funds that lawmakers had designated for other purposes to finance the construction of the wall. The move came on the same day that Mr. Trump confirmed that the national emergency he had declared almost exactly a year ago to allow him to take money Congress had allocated for other purposes and spend it on the border wall would remain in place for another year.

The Pentagon’s decision to divert funds was greeted on Thursday with criticism by a few prominent members of Mr. Trump’s party, who joined Democrats in saying the president’s team had overstepped its constitutional authority by second-guessing congressional spending decisions.

“Once those choices have been made, the Department of Defense cannot change them in pursuit of their own priorities without the approval of Congress,” said Representative Mac Thornberry of Texas, the top Republican on the House Armed Services Committee. “Attempts to do so undermines the principle of civilian control of the military and is in violation of the separation of powers within the Constitution.”