"That’s not what I said. That’s what people said that I said," he told a skeptical Wallace early in the interview.

"Can I see how people took that the wrong way? Absolutely," Mulvaney later said in the interview. "But I never said there was a quid pro quo because there isn’t."

Exclusively on FOX News Sunday Mick Mulvaney responds to critics of his press briefing appearance. Mulvaney says "his language never said quid pro quo" in regards to his remarks on U.S. aid to Ukraine. @FNS pic.twitter.com/zsgmqDwOq1 — FoxNewsSunday (@FoxNewsSunday) October 20, 2019

Wallace challenged Mulvaney on that point, saying he believed "that anyone listening to what you said in that briefing could only come to one conclusion."

Fox then replayed video of Mulvaney's Thursday press conference, during which Wallace pointed out that Mulvaney listed three reasons, not the two he listed on Sunday, for why the aid had been withheld.

"You were asked specifically by Jonathan Karl, was investigating Democrats one of the conditions for holding up the aide? Was that part of the quid pro quo? And you said, it happens all the time," Wallace said, referring to the ABC reporter who had questioned Mulvaney on Thursday.

Mulvaney said Trump mentioned the investigations in passing, but the chief of staff then stuck to his position that corruption and ensuring that aid was provided by other countries were the reasons for the delayed aid.

Wallace then pressed Mulvaney again.

"You know, I hate to go through this, but you said what you said. And the fact is, after that exchange with Jonathan Karl, you were asked another time why the aid was held up. What was the condition for the aid? And you didn't mention two conditions. You mentioned three conditions," Wallace said.

Wallace then showed video of Mulvaney saying "three issues for that" while holding up three countries during the Thursday press conference. The third issue cited by Mulvaney on Thursday was whether Ukraine was cooperating with an ongoing investigation by the Justice Department.

The Justice Department has said the linking of Ukraine aid to its investigation was "news to us," according to a senior Justice official cited by Fox.