"I never said there was a quid pro quo because there isn't," Mulvaney told "Fox News Sunday," using a Latin phrase meaning a favour for a favour.

Mulvaney told reporters on Thursday that Trump's decision to withhold $US391 million in aid to Ukraine was linked in part to his desire for an investigation by Kiev into a debunked theory that a Democratic National Committee (DNC) computer server was held in Ukraine.

When told by a reporter that what he had just described was a quid pro quo, Mulvaney responded: "We do that all the time with foreign policy."

His remarks at a White House news conference created turmoil in Washington and left the president's Republican allies flummoxed and frustrated.

Mulvaney walked back the comments in a statement the same day. But after weeks in which the president argued that he had done nothing wrong, Mulvaney's remarks undermined the core arguments that Trump and his advisers have made against the effort to oust him from office in a House of Representatives impeachment inquiry.

"This Scam going on right now by the Democrats against the Republican Party, and me, was all about a perfect phone call I had with the Ukrainian President. He's already stated, NO PRESSURE!" Trump said as part of a series of tweets later on Sunday.

Mulvaney said on Sunday he did not offer to resign over the episode, nor was his possible resignation discussed at the White House.

"Absolutely, positively not," he told Fox News Sunday. "I'm very happy working there. Did I have the perfect press conference, no, but again the facts are on our side. ... I still think I'm doing a pretty good job as the chief of staff and I think the president agrees."

US Secretary of State Mike Pompeo on Sunday supported Mulvaney's walk-back of his remarks, saying he had not seen evidence of a connection between withholding Ukraine aid and Kiev pursuing a political investigation.

Australian Associated Press