"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 said in a statement.
In a letter released on Tuesday, the three chairmen of the House committees conducting the probe wrote, "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," the letter read.
Rep. Adam Schiff, the House Intelligence Committee chairman, Rep. Eliot Engel, the House Foreign Affairs Committee chairman, and Rep. Carolyn Maloney, the acting chairwoman of the House Oversight Committee, said Mulvaney may have been involved in "efforts to cover up these activities."
At a now infamous Oct. 17 White House press briefing, Mulvaney admitted to a quid pro quo in an exchange with ABC News Chief White House Correspondent Jonathan Karl, saying military aid was withheld to get Ukraine to probe Democrats.
"So the demand for an investigation into the Democrats was part of the reason that he ordered you to withhold funding to Ukraine?" Karl asked.
"'Look back to what happened in 2016,' certainly was part of the thing that he was worried about in corruption with the nation," Mulvaney said. "And that is absolutely equivalent."
"What you described is a quid pro quo," Karl pressed. "It is: Funding will not flow unless the investigation into the Democrats' server happens as well."
"We do that all the time with foreign policy," Mulvaney answered.
"I have news for everybody: Get over it," he continued.
"There's going to be political influence in foreign policy," Mulvaney said. "That is going to happen. Elections have consequences and foreign policy is going to change from the Obama administration to the Trump administration."
Later that day, Mulvaney said in a statement that the news media had misconstrued his words.
The Democrats' letter calls on Mulvaney to appear Nov. 8.
There was no immediate response from Mulvaney or White House lawyers. The White House has directed all administration officials not to cooperate with the Demorats' impeachment probe, casting it as "illegitimate" and "unfair."
The Democratic chairs noted in their letter that Mulvaney ignored an Oct. 4 subpoena for key White House documents.
ABC News' Ben Gittleson contributed reporting to this article.