House committees leading the impeachment inquiry into President Trump have requested that acting White House Chief of Staff Mick Mulvaney appear before the panels for a deposition on Friday, claiming that he was “directly involved” in the Ukraine controversy which sparked the proceedings.

House Intelligence Committee Chair Adam Schiff, Oversight Committee acting Chair Carolyn Maloney and Foreign Affairs Committee Chair Eliot Engel penned a letter to Mulvaney on Tuesday, requesting his appearance at a deposition as part of the impeachment inquiry this Friday at 9 a.m.

NEW DEPOSITION TRANSCRIPTS RELEASED

“Based on evidence gathered in the impeachment inquiry and public reporting, we believe that you possess substantial first-hand knowledge and information relevant to the House’s impeachment inquiry,” they wrote.

The White House appeared to reject the request Tuesday.

"Past Democrat and Republican administrations would not be inclined to permit senior advisers to the president to participate in such a ridiculous, partisan, illegitimate proceeding – and neither is this one,” White House deputy press secretary Hogan Gidley told reporters.

The request for Mulvaney’s deposition comes amid the House’s formal impeachment inquiry into the president. The inquiry was opened in September after a whistleblower complaint alleged that Trump, during a July phone call, pushed Zelensky to investigate former Vice President Joe Biden and his son Hunter as military aid to the country was being withheld.

“Specifically, the investigation has revealed that you may have been directly involved in an effort orchestrated by President Trump, his personal agent, Rudolph Giuliani, and others to withhold a coveted White House meeting and nearly $400 million in security assistance in order to pressure Ukrainian President Volodymyr Zelensky to pursue investigations that would benefit President Trump’s personal political interests, and jeopardized our national security in attempting to do so,” the Democrats said in their letter.

A transcript released by the White House shows Trump making that request, but he and his allies deny that military aid was clearly linked to the request or that there was any "quid pro quo." Some witnesses coming before House committees as part of the impeachment proceedings have challenged that assertion.

In the letter, Schiff, D-Calif., Maloney, D-N.Y., and Engel, D-N.Y., referenced “evidence,” such as comments made by former White House National Security Adviser John Bolton regarding Mulvaney’s role in Trump’s conversations with Zelensky.

“…Bolton told a National Security Council staffer ‘to notify the chief lawyer for the National Security Council about a rogue effort by Mr. [Gordon] Sondland, Mr. Giuliani, and Mick Mulvaney’ to pressure Ukraine for political help,” they wrote.

“Ambassador Bolton, who appears to have believed that you were directly involved in the President’s scheme, reportedly instructed the NSC staffer to tell the NSC lawyers, ‘I am not part of whatever drug deal Sondland and Mulvaney are cooking up,’” they wrote. “The ‘drug deal’ appears to be a reference to the scheme to pressure Ukraine to pursue the investigations for the political benefit of President Trump.”

The chairs also accused Mulvaney of playing “a central role” in the president’s move to withhold military aid from Ukraine, and criticized him for his response to questions about the funds during a press conference at the White House last month.

“You admitted publicly that President Trump ordered the hold on Ukraine security assistance to further the President’s own personal, political interests, rather than national interest,” they wrote.

During a press conference on Oct. 17, Mulvaney was asked why Trump ordered the hold on military aid. The White House’s position has consistently been that there was no evidence of a quid pro quo with regard to the aid. But during that appearance, Mulvaney seemed to depart from his talking points.

“We do that all the time with foreign policy,” Mulvaney said. “And I have news for everybody: Get over it. There’s going to be political influence in foreign policy.”

Mulvaney, for days, tried to walk back his statement, after critics claimed he acknowledged a "quid pro quo," but the chairs blasted his efforts Tuesday.

“Despite your subsequent attempts to walk-back this clear admission, your statements to the American public on October 17 were nothing less than a televised confession that President Trump’s order to freeze Ukraine security assistance was explicitly linked to Ukraine pursuing investigations as part of an effort to bolster the President’s 2020 re-election campaign,” they wrote.

It is unclear, at this point, whether Mulvaney will appear before the committees on Friday. The White House did not immediately respond to Fox News' request for comment.

Fox News' Chad Pergram and John Roberts contributed to this report.