White House press secretary Sean Spicer. Chip Somodevilla/Getty Images CNN on Tuesday rebutted White House press secretary Sean Spicer's suggestion that the cable news network had walked back comments about a top adviser's credibility.

The New York Times reported earlier this week that CNN's "State of the Union" passed up the opportunity to interview Kellyanne Conway, a top adviser to President Donald Trump, in part over "serious questions about her credibility."

During Tuesday's press briefing, Spicer said CNN had backed off its comments on Conway.

"My understanding is they retracted that, they've walked that back or denied it — however you want to put it, I don't care," Spicer told reporters. "But I think Kellyanne is a very trusted aide of the president. I think for any characterization otherwise is insulting."

He continued: "If they choose not to work with someone, that's up to them, but I think we're gonna continue to put out key leaders to this administration, including Kellyanne, that can articulate the president's policies and agenda."

But CNN's communications team denied any retraction, tweeting shortly after Spicer's comments: "CNN was clear, on the record, about our concerns about Kellyanne Conway's credibility, to The New York Times and others. We have not 'retracted' nor 'walked back' those comments. Those are the facts."

Conway herself denied the Times report in a tweet on Monday, saying she was unavailable for the CNN interview on Sunday and was invited to the network on Monday and Tuesday.

"I could do no live Sunday shows this week [because] of family," she said. "Plus, I was invited onto CNN today & tomorrow. CNN brass on those emails."

Some journalists and media commentators have recently suggested that networks should not book Conway, saying she tells falsehoods so frequently that networks can't rely on her to share accurate information about the administration.

Conway made headlines last week when she repeatedly cited a nonexistent massacre in Bowling Green, Kentucky, to justify Trump's executive order temporarily barring people from seven majority-Muslim countries from entering the US.

Amid the back and forth, Conway is set to appear on "The Lead" with Jake Tapper on the network later Tuesday.

Maxwell Tani contributed to this report.