WASHINGTON — House impeachment investigators on Tuesday called on Mick Mulvaney, the White House’s acting chief of staff, to testify this week in their inquiry into President Trump’s pressure campaign on Ukraine, closing in on the upper echelons of Mr. Trump’s staff as they near the end of their fact-finding phase.

Mr. Mulvaney has emerged as a central figure in House Democrats’ investigation because of his proximity to the president as well as his own actions. He undercut Mr. Trump’s repeated denials of a quid pro quo when he admitted at a news conference weeks ago that the White House withheld nearly $400 million in military aid to Ukraine to further the president’s political interests.

“I have news for everybody: Get over it,” he told reporters at the time. “There’s going to be political influence in foreign policy.” He backtracked hours later and tried to deny that he had ever confirmed such an arrangement.

Mr. Mulvaney, who has remained defiant throughout the inquiry, is unlikely to cooperate with House investigators. He ignored a subpoena issued last month from House investigators for documents related to the inquiry, and his top aide, Robert Blair, refused to comply with a subpoena to testify this week.