The top two Republicans and Democrats on the congressional appropriations committees are quietly protesting the White House’s decision to take down a special website tracking federal spending, escalating a battle between Congress and President Trump over spending powers.

In a previously undisclosed letter sent last month to Russell T. Vought, the director of the Office of Management and Budget, the lawmakers questioned the rationale for shutting down the website, which they and advocacy groups said was a violation of the law.

“We look forward to working with you to restore public access to apportionment data in accordance with statute,” they wrote.

The letter was signed by Representative Tom Cole of Oklahoma and Senator Susan Collins of Maine, the Republican chairs of the House and Senate appropriations committees, and the two senior Democrats on those panels, Representative Rosa DeLauro of Connecticut and Senator Patty Murray of Washington.

It was a rare instance of bipartisan pushback from members of both the House and the Senate against the White House for its actions, at a time when the Trump administration is mounting an aggressive challenge to the legislative branch’s spending prerogatives.

Mr. Cole’s signature was a particularly significant development since he had not joined in a previous bipartisan congressional letter taking Mr. Trump’s budget office to task on spending issues. In a brief interview on Monday, he said he believed the website should be restored, a view shared by Ms. Collins.