Washington • House Democrats investigating whether to impeach President Donald Trump issued a subpoena Monday demanding that Rudy Giuliani, his private lawyer, produce communications and other records related to his attempts to pressure Ukraine to investigate the president’s Democratic rivals.

The new demands of Giuliani and separate requests sent to three of his associates said to be involved in the Ukraine matter suggest that Democrats are moving quickly to stand up their investigation, even as Trump on Monday questioned whether the chairman leading their impeachment inquiry, Rep. Adam B. Schiff, should be arrested for treason.

“Our inquiry includes an investigation of credible allegations that you acted as an agent of the president in a scheme to advance his personal political interests by abusing the power of the office of the president,” Schiff and two fellow Democratic chairmen, Rep. Elijah E. Cummings of the Oversight and Reform Committee and Rep. Eliot L. Engel of the Foreign Affairs Committee, wrote in a letter to Giuliani.

Democrats said they had also sent letters requesting documentary evidence and to schedule depositions in the coming two weeks with three associates of Giuliani: Lev Parnas, Igor Fruman and Semyon Kislin.

The requests follow another subpoena sent Friday to Secretary of State Mike Pompeo for documents, and a request that he make five department officials available for depositions in the coming days.

But in targeting Giuliani directly for a long list of possible communications, Democrats are now aiming at the man who appears to be at the center of the pressure campaign on Ukraine. Giuliani is mentioned frequently in a government whistleblower complaint that set off the House inquiry and in recent weeks, he has admitted in interviews to taking a series of actions to advance investigations in Ukraine into Democrats, including Joe Biden, a leading candidate for president.

The Democrats asked for a wide range of communications and documents going back to January 2017.

Giuliani did not immediately respond to a request for comment.

But like a growing list of potential witnesses, he will now face an excruciating choice: Either he can hand over material under subpoena that could help build the case against the president, or refuse and feed a possible impeachment article based on obstruction of Congress. The chairmen gave Giuliani about two weeks, until Oct. 15, to comply.

“Your failure or refusal to comply with the subpoena, including at the direction or behest of the president or the White House, shall constitute evidence of obstruction of the House’s impeachment inquiry and may be used as an adverse inference against you and the president,” they wrote.

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The new requests came as Democrats were preparing to hold closed-door depositions this week with State Department officials connected to the Ukraine matter, as well as a closed hearing with the intelligence community inspector general who fielded the whistleblower’s complaint.

The new subpoenas — and Trump’s threat to Schiff, who leads the Intelligence Committee — came as both sides continued to dig in Monday for what could be a protracted and ugly fight over the fate of Trump’s presidency. Republicans rushed to publicly defend Trump and shift attention back onto unsubstantiated accusations of wrongdoing by Democrats in Ukraine. Democrats framed the president’s remarks as a desperate attempt to confuse voters about the charges against him and discourage potential witnesses from cooperating with their inquiry.

In a sign that Washington is not preparing for a resolution anytime soon, Sen. Mitch McConnell, R-Ky., the Senate majority leader, said Monday for the first time since the Ukraine revelations burst into public that if the House ultimately voted to impeach the president, a Senate trial would be unavoidable.