Mr. Trump personally ordered his staff to freeze the aid just days before a now infamous July call in which he asked President Volodymyr Zelensky of Ukraine to do him “a favor” and help investigate Mr. Biden and a conspiracy theory about Ukrainian meddling in the 2016 election. He lifted a block on its delivery in September only under intense bipartisan pressure from Congress, where lawmakers view the money as vital to combating Russia’s armed aggression in the region.

The White House has denied that the aid was being withheld to exert leverage over the Ukrainians, but at least one senior diplomat worried privately that that was precisely what was happening, and the administration has been unwilling to answer questions about the timeline and rationale for the decision. Regardless of the reasoning, the decision to withhold aid that was allocated by Congress on a bipartisan basis prompted confusion and concern within the State and Defense Departments, which were responsible for delivering the money, as well as among lawmakers in both parties who had a hand in allocating it.

Democrats leading the impeachment inquiry in the House suspect the actions may be related. They point to comments in early September by Vice President Mike Pence, who said publicly that a review of the funds was based on White House concerns about “issues of corruption.”

“The enclosed subpoena demands documents that are necessary for the committees to examine this sequence of these events and the reasons behind the White House’s decision to withhold critical military assistance to Ukraine that was appropriated by Congress to counter Russian aggression,” read the letters accompanying the subpoenas, signed by Representative Adam B. Schiff, the chairman of the Intelligence Committee; Representative Elijah E. Cummings, the chairman of the Oversight and Reform Committee; and Representative Eliot L. Engel, the chairman of the Foreign Affairs Committee.

The Defense Department had been anticipating a subpoena. Last week, the Pentagon’s general counsel directed all department heads to collect and turn in all documents and material related to military aid to Ukraine.

“As we’ve stated previously, we are prepared to work with Congress and other relevant parties on questions related to the issue of Ukrainian aid as appropriate,” Lt. Col. Carla M. Gleason, a Pentagon spokeswoman, said on Monday.

The budget office did not reply to a request for comment. The House Appropriations and Budget Committees are reviewing some documents produced by the budget office in response to a separate request the two committees sent in late September about the delay in the foreign aid, aides said on Monday.