WASHINGTON — The House threatened on Wednesday to subpoena the White House if it did not comply by Friday with requests for a broad range of documents related to President Trump’s efforts to pressure Ukraine into investigating Joseph R. Biden Jr. and his son.

Representative Elijah E. Cummings of Maryland, the chairman of the Oversight and Reform Committee, notified his committee of the impending subpoena on Wednesday. He said the White House had thus far ignored Congress’s voluntary requests.

“I do not take this step lightly,” Mr. Cummings wrote. “Over the past several weeks, the committees tried several times to obtain voluntary compliance with our requests for documents, but the White House has refused to engage with — or even respond to — the committees.”

The subpoena threat came as House Democratic leaders were preparing to lay out the next steps in their rapidly unfolding impeachment inquiry, and as lawmakers expected to hear a mysterious bit of new information abruptly offered up by the State Department’s independent watchdog.

After a Wednesday morning news conference where Speaker Nancy Pelosi and Representative Adam B. Schiff, the chairman of the Intelligence Committee, planned to outline the progress of their inquiry, Steven A. Linick, the State Department’s inspector general, was to brief lawmakers in the afternoon about urgent material he said was relevant to the investigation.

It promised to be another momentous day in Washington, where in just over two weeks, revelations about attempts by Mr. Trump and his private lawyer to pressure Ukraine to help smear Mr. Biden, a Democratic political rival, have touched off an inquiry that threatens his presidency. The House inquiry is reshaping the political landscape and could have profound consequences for an already deeply polarized country.

What exactly the inspector general, Steve A. Linick, intended to share with Congress remained a matter of intense speculation early on Wednesday. Mr. Linick, who was not believed to be investigating the Ukraine matter himself, contacted lawmakers early Tuesday afternoon and extended a cryptic and urgent invitation to meet the next day “to discuss and provide staff with copies of documents,” according to an invitation reviewed by The New York Times.

The invitation noted only that the documents had been shared with Mr. Linick by the State Department’s acting legal adviser.

Inspectors general frequently share information with Congress, but lawmakers and other government officials familiar with the process said Mr. Linick’s request was highly unusual, particularly given the extraordinary political pressure surrounding the State Department and Ukraine.

On Tuesday, Secretary of State Mike Pompeo became one of the first Trump administration officials to throw himself on the gears of churning House investigation, writing in a letter to Democratic chairmen that their demands for confidential interviews with diplomats with knowledge of the case was an “an act of intimidation” and would not be immediately met.

But instead of bringing it to a halt, Mr. Pompeo’s actions seem only to have fueled the case. The Democrats said any attempt to block witnesses from speaking to Congress would be construed by them as witness intimidation. And at least two of the diplomats Mr. Pompeo objected to speaking had indicated to the House that they would appear for private depositions anyway.

Late Tuesday, the chairmen wrote to Mr. Pompeo’s deputy saying the secretary had an “obvious conflict of interest” in light of news reports that he listened in on the July phone call.

“Given the secretary’s own potential role, and reports of other State Department officials being involved in or knowledgeable of the events under investigation,” they wrote, “the committee may infer that he is trying to cover up illicit activity and misconduct, including by the president.”

On Wednesday, in Rome, Mr. Pompeo confirmed for the first time that he had been listening in on the call.

“I was on the phone call,” he said at a news conference in the Italian capital.