Mr. Mulvaney told reporters last month that the aid was suspended in part to force Ukraine to investigate a conspiracy theory about supposed Ukrainian help for Democrats in the 2016 presidential election, a theory that the president’s onetime homeland security adviser, Thomas P. Bossert, had repeatedly told him was “completely debunked.” Hours after Mr. Mulvaney’s comment to reporters confirming a direct link between the aid and the president’s personal political interests, the chief of staff tried to take it back, issuing a statement saying that was not what he meant.

House investigators issued a subpoena to Mr. Mulvaney late Thursday, but he failed to show up for a House deposition scheduled for the next morning. Hours later, his lawyers went to court.

Mr. Mulvaney initially resisted getting outside legal help after some of his allies told him he did not need it. But as House Republicans have indicated that they may focus on Mr. Mulvaney’s role in the pressure campaign on Ukraine, possibly blaming him rather than the president, it has become clear that the chief of staff’s own interests may be in conflict with the White House on this issue.

That left Mr. Mulvaney in the awkward position of not wanting to openly defy the White House counsel, but also not wanting to imperil himself with a possible contempt citation for ignoring a subpoena. So far, a dozen current administration officials have testified despite the White House edict, while about 10 have refused to talk or provide documents.

The White House declined to comment on the record on Saturday, but an administration official who insisted on anonymity said the legal action Mr. Mulvaney’s lawyers filed was simply a way to determine whether to comply with the House. Mr. Mulvaney, the official said, has as much right as any other American to seek relief in the courts.

A House Democratic aide, likewise declining to be identified, said the committees leading the inquiry would not be deterred and argued that because Mr. Mulvaney had discussed the matter in the news media, he had little justification to claim confidentiality when it came to the House proceedings.

Mr. Trump has grown increasingly sour on Mr. Mulvaney in recent months, according to White House insiders. The president has technically not even made Mr. Mulvaney his official chief of staff, leaving an “acting” modifier in front of the title for more than 10 months (another never-before).