The three congressional committees probing whether President Donald Trump should be impeached on Tuesday called on acting White House chief of staff Mick Mulvaney to testify in the inquiry.

Mulvaney is unlikely to comply with the request that he appear for a deposition on Friday. The White House has directed senior officials not to participate in the impeachment investigation, which Trump has attacked as illegitimate.

Late Tuesday afternoon, a White House spokesman responded to the request by telling NBC News, "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."

In a letter to Mulvaney on Tuesday, the chairs of the House Intelligence, Foreign Affairs and Government Oversight committees wrote that, "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.

"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 committee chairs wrote.

Mulvaney ignited a firestorm last month when he appeared to confirm during a White House news conference, on camera, that Trump had withheld nearly $400 million in congressionally appropriated military aid to Ukraine, in order to force that country to open an investigation into a discredited conspiracy theory about the 2016 election.

The halting of aid came in connection with "an ongoing investigation into the 2016 election," and the possibility that a Democratic National Committee server that investigators have said was hacked by Russian agents ended up in Ukraine.

While Mulvaney did not himself use the term "quid pro quo" at the time, when he was told by a reporter that the situation of withholding aid to get Ukraine to conduct a probe at Trump's request was in fact a quid pro quo, Mulvaney said, "We do that all the time."

Mulvaney later sought to walk back his previous statement, claiming his words had been taken out of context.

Tuesday's letter came just a day after one of Mulvaney's top aides, Robert Blair, defied a subpoena issued by the committees investigating a potential impeachment of Trump. The subpoena had sought to compel Blair's testimony.

Blair is one of the few people who actually listened to a controversial July 25 call between Trump and Zalensky, in which Trump asked his Ukrainian counterpart for "a favor."

Like Mulvaney, Blair is also believed to have specific information about a halt to U.S. military aid earmarked for Ukraine, which was ordered by Trump and conveyed through Mulvaney.

This story has been updated to include the White House's response to the request.

— CNBC's Dan Mangan and Kevin Breuninger contributed to this story.