WASHINGTON — House investigators pounded the Trump administration and its allies on Thursday with new subpoenas, demanding documents from Rick Perry, the energy secretary, and testimony from two more witnesses as they aggressively challenged a White House pledge to starve their impeachment inquiry of evidence.

Three Democratic chairmen leading the inquiry instructed Mr. Perry to turn over by next Friday any records that would shed light on President Trump’s attempts to pressure the Ukrainian government to open corruption investigations into former Vice President Joseph R. Biden Jr. and his son. Investigators also want answers on whether Mr. Perry tried to influence the management of Ukraine’s state-owned gas company.

Hours earlier, they demanded that two businessmen, Lev Parnas and Igor Fruman, appear for depositions next Wednesday and hand over records related to their work with Rudolph W. Giuliani, Mr. Trump’s personal lawyer. Mr. Giuliani has been the point man in the president’s pressure campaign on Ukraine, around which the inquiry is centered. The subpoenas came shortly after the two men were indicted on federal campaign finance charges that touched on their work in Ukraine.

The new subpoenas, and more in the works, sent a clear message to the White House that Democrats do not intend to back down from a growing constitutional clash over their inquiry, even after the White House defiantly said this week that it would stonewall all requests for witnesses and documents.