WASHINGTON — Democrats moved assertively on Monday to increase political pressure on the White House and congressional Republicans to furnish documentation about explosive allegations that President Trump sought to pressure the Ukrainian president to help produce damaging information on a leading political rival.

In the House, where the revelations about a conversation between Mr. Trump and the Ukrainian leader, Volodymyr Zelensky, were fueling new calls for impeachment, the chairmen of three committees investigating the matter threatened to issue subpoenas in the coming days if the administration did not hand over a transcript of the call and a related whistle-blower complaint.

Mr. Trump acknowledged on Sunday that he had leveled allegations of corruption against former Vice President Joseph R. Biden Jr. with Mr. Zelensky, but on Monday, he denied that he had pressured the Ukrainian president to investigate and used a package of hundreds of millions of dollars in security aid as leverage. Mr. Trump has defended the conversation as entirely appropriate.

Still, Democrats are demanding to see evidence. On Monday, they said a failure by the administration to disclose a complaint about Mr. Trump’s interactions with Mr. Zelensky would be considered obstruction, an indication that they could consider it as grounds for impeachment.