CNN anchor Jake Tapper and President Trump’s counselor, Kellyanne Conway, went toe-to-toe in a 25-minute-long interview on Tuesday that was punctuated by several heated exchanges over the accuracy of statements the president has made and the media’s treatment of Trump.The tense interview comes after CNN says it declined to have Conway on Tapper’s Sunday show, “State of the Union,” because of concerns over her credibility.White House spokesman Sean Spicer said Tuesday that CNN had retracted its statement, but the network fired back, saying it stood by its concerns about Conway.Tapper and Conway did not broach that conflict but touched on several other dustups between the media and the Trump administration that have colored the first few weeks of Trump’s presidency.Tapper repeatedly sought to hold Conway accountable for the Trump administration dismissing press reports it doesn’t like as fake news.He noted that Conway has had to apologize for claiming that a massacre took place in Bowling Green, Ky., when in fact it was merely the spot where a couple of would-be terrorists were arrested for hatching a scheme.“It is difficult to hear criticism from the White House, which has such little regard day in, day out, for facts, for truth and who calls us fake news for stories that they don't like,” Tapper said.Conway kept her composure and repeatedly sought to offer an “olive branch” to CNN and other media outlets that have been butting heads with Trump and his aides ever since the campaign.But she also vented frustration with the coverage the White House gets, insisting it is always negative and that the “palace intrigue” stories about the power dynamics within the administration are almost always false.“Think about how small our staff was and how small our budget was for a presidential campaign, Jake, that succeeded and saw things other people didn't see,” Conway said. “We breathe each other's oxygen in the foxhole. We are all very close. All the stories for a White House that is constant action, constant movement — they're just not true.”Tapper asked Conway directly if she believes CNN is “fake news.”“I don't think CNN is fake news,” she responded. “I think there are some reports everywhere, in print, on TV, on radio, in conversation that are not well researched and are sometimes based on falseness and are actually hurtful.”Tapper also ripped Trump for claiming that the news media has failed to cover international terrorist attacks because it harbors a secret agenda, arguing that CNN has reporters active in terrorist hotspots around the world putting their lives at risk to report on those incidents.“He was saying the media does not cover these stories because we don't want to cover them because we have some sort of agenda,” Tapper said. “That's what he was suggesting and it's offensive given the fact that CNN and other media organizations have reporters in danger right now in war zones covering [the Islamic State in Iraq and Syria]. And I just don't understand how the president can make an attack like that.”Conway acknowledged CNN’s coverage of several high-profile terror attacks but argued that the media remains obsessed with covering Trump as if the campaign is still going on and that it could do a better job of framing the threat of radical Islam.“There seems to be some coverage these days, maybe not here, but definitely elsewhere that somehow terrorism is not a big problem, or somehow national security is all taken care of and that's just not true,” Conway said. “I think when you're talking about extreme vetting, he is making the point that that is in response to the threat of terrorism globally.”