Acting White House chief of staff Mick Mulvaney on Sunday denied ever saying that there had been a "quid pro quo" in the release of military aid to Ukraine, days after sparking an uproar by appearing to acknowledge exactly that during a news briefing.

Citing concerns about corruption, Mulvaney said Thursday that one reason the aid was held up was because of President Donald Trump's wish for an investigation into a theory that Ukraine, not Russia, was behind the theft of Democratic National Committee emails in 2016. Trump has insisted on pursuing that theory despite the unanimous conclusion of the U.S. intelligence community that Russia was behind the hack.

"Fox News Sunday" host Chris Wallace asked Mulvaney why he said "that aid to Ukraine depended on investigating the Democrats." Mulvaney denied that was what he had said.

"That's what people said I said," he told Wallace. Mulvaney claimed "people got sidetracked" at the news conference and that he had said the aid was withheld for two reasons: corruption concerns and to pressure European nations into giving Ukraine more aid.

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He said the president had mentioned the Democratic National Committee server "from time to time" but "it wasn't connected to the aid."

But Wallace was unpersuaded, telling Mulvaney, "I believe that anyone listening to what you said in that briefing could come to only one conclusion."

"No, you totally said that," Wallace said.

Speaking on CNN's "State of the Union" on Sunday, Rep. Francis Rooney, R-Fla., was also skeptical of Mulvaney's attempt to retract his comments.

"I don't see how you walk back something that's clear," Rooney said. "I would say, 'game, set, match' on that."

On Friday, Rooney made headlines as a Republican House members who said he wouldn't rule out voting to impeach Trump. The next day, Rooney announced he would not seek reelection.

"I'm going to be looking at myself in the mirror and my children a lot longer than anybody in the Capitol," Rooney said Sunday. "And it's important to have integrity in what you say and do."

Trump is currently facing an impeachment inquiry over allegations that he used the military aid as leverage to pressure Ukraine into investigating former Vice President Joe Biden, a leading candidate in the 2020 race.

Although Mulvaney denied the demand for a Biden probe was ever connected to the aid, his apparent admission that it had been withheld in part because of Trump's push for an investigation into the 2016 election sparked an uproar because it contradicted the administration's earlier position that there had been no kind of "quid pro quo."

Mulvaney, who also retracted his news conference comments in a statement last week, repeated his assertion that the aid had been held up over corruption and to push other countries to help. He said the funds were released after conducting "research on other countries’ aid to Ukraine" and they were satisfied that corruption was being addressed.

"There was never any connection between the flow of money and the server," Mulvaney said.

"Mick, you know, I hate to go through this, but you said what you said," Wallace told Mulvaney. He said that later in the news conference Mulvaney had explicitly listed an investigation into the DNC server as a third reason for withholding aid.

Mulvaney said he "didn't speak clearly" and "folks misinterpreted what I said."

Wallace asked if Mulvaney had ever considered submitting his resignation amid the blowback from the news conference.

"No, absolutely not," he said. "I’m very happy working there. Did I have the perfect press conference? No. But again, the facts were on our side."

Tom Bossert, Trump's former homeland security adviser, has said the notion that Ukraine was behind the DNC hack "has no validity."

"It’s not only a conspiracy theory, it is completely debunked," Bossert said last month on ABC News' "This Week."

Bossert said he was "deeply frustrated" with people "repeating that debunked theory to the president. It sticks in his mind when he hears it over and over again."