Acting White House chief of staff Mick Mulvaney insisted Sunday that he did not say that President Donald Trump held up military aid for Ukraine for political purposes — despite acknowledging the issue at the heart of House Democrats' impeachment inquiry during a televised press conference.

"I'm flinching because that's what people are saying that I said, but I didn't say that," Mulvaney told "Fox News Sunday" host Chris Wallace of the comments he made — and then walked back in a contradictory statement — Thursday.

"There were two reasons that we held up the aid," he continued. "We've talked about this at some length. The first one was the rampant corruption in Ukraine. The president was also concerned about whether or not other nations, specifically European nations, were helping with foreign aid to Ukraine as well."

Mulvaney, who is also the director of the Office of Management and Budget, added that he had discussed in the past with the president a debunked conspiracy theory about a Democratic National Committee email server hidden in Ukraine, but said, "it wasn't connected to the aid"

"And that's where I think people got sidetracked this weekend at that press conference," he said. "Two reasons for holding back the aid."

Wallace interjected, saying he believed "anyone listening to what you said in that briefing could only come to one conclusion." Wallace then played a tape of Mulvaney's remarks from Thursday, when the acting chief of staff said the nearly $400 million in Congress-approved security aid for Ukraine was held up because Trump is skeptical about foreign aid, had concerns about corruption, and wanted Ukraine to probe a debunked conspiracy involving the 2016 U.S. election.

"So the demand for an investigation into the Democrats was part of the reason he ordered to withhold funding to Ukraine?" ABC's Jonathan Karl asked.

"The look back to what happened in 2016 certainly was part of the thing he was worried about in corruption with that nation, and that is absolutely appropriate," Mulvaney said.

Karl pressed Mulvaney, saying, "To be clear: what you just described is a quid pro quo. It is 'funding will not flow unless the investigation into the Democratic server happened, as well.'"

"We do that all the time with foreign policy," Mulvaney responded, adding that the administration had also held up money to three Central American countries so that they would change their immigration policies.

"Get over it," he said. "There's going to be political influence in foreign policy."

The clip Wallace showed ended after Mulvaney's "We do that all the time" remarks, to which Mulvaney told Wallace to watch what he said before that comment.

"No, you totally said that," Wallace shot back, highlighting Mulvaney's linking of the military aid to the politically advantageous probe.

At the time, Mulvaney's acknowledgment that the aid had been withheld for political reasons angered and confused Trump allies inside and outside the administration, according to two people familiar with the matter. One of them called Mulvaney’s comments in the White House briefing room "an unmitigated disaster."

For the past month, Trump and allies have insisted no quid pro quo took place regarding Ukraine. House Democrats opened an impeachment inquiry into the president after a whistleblower filed a complaint over Trump's July 25 phone conversation with Ukrainian President Volodymyr Zelenskiy and the administration's subsequent response.

In a White House summary of the call, Trump asked Zelenskiy for a "favor" shortly after the latter discussed U.S. military aid. That favor included asking Zelesnkiy to probe the conspiracy theory about a Democratic National Committee email server, as well as former Vice President Joe Biden and his son Hunter Biden.

Mulvaney on Thursday insisted that the holdup had "absolutely nothing to do with Biden."

"I was involved with the process by which the money was held up temporarily, OK?" Mulvaney said. "Three issues for that. The corruption in the country, whether or not other countries were participating in the support of the Ukraine, and whether or not they were cooperating in an ongoing investigation with our Department of Justice. That's completely legitimate."

A senior Justice Department official said in response: "If the White House was withholding aid from Ukraine with regard to any investigation by the Justice Department, that’s news to us."

Mulvaney then walked his remarks back later that day, saying in a statement: "There was absolutely no quid pro quo between Ukrainian military aid and any investigation into the 2016 election."

The debunked DNC server conspiracy — known as "CrowdStrike" — seeks to distance Russia from culpability in the hacking of Democratic National Committee emails. CrowdStrike is a cybersecurity firm that investigated the hacking, and the conspiracy theory paints its findings about Russia's hacking efforts as suspect and politically motivated.

Last month, Trump's former homeland security adviser, Tom Bossert, told ABC's "This Week" that the theory is "not only a conspiracy, it is completely debunked," adding that "it has no validity."

"Can I see how people took that the wrong way? Absolutely," Mulvaney said Sunday. "But I never said there was a quid pro quo cause there isn't."

Mulvaney also told Wallace that he "absolutely positively" did not consider resigning after Thursday's uproar.

"I'm very happy working there," he said. "Did I have the perfect press conference? No. But again, the facts are on our side."

He said he believes he is still "doing a pretty good job as the chief of staff and I think the president agrees."

Secretary of State Mike Pompeo, asked Sunday on "This Week" about Mulvaney's comments, said: "I will leave to the chief of staff to explain what it is he said and what he intended."