"I saw a man who is a political genius", Miller said, adding that as a candidate, Trump had "tapped into something magical that is happening in the heart of this country". "He should have known they are duplicitous, cunning and not our friends".
"Not only do I think [the tweets] help, but I think in the toxic environment that you've created here in CNN and cable news, which is a real crisis of legitimacy for your network - and we saw it, of course, with the extremely fake news that you reported about the Don Jr. and WikiLeaks story".
The very public apology was just the latest fallout from the release of "Fire and Fury", in which Wolff claims, after having had access to the West Wing during the first months of the Trump administration, that numerous president's top aides and confidants consider him paranoid, inept and even unfit to hold office.
Its publication prompted Trump to post on Twitter on Saturday that he is a "very stable genius".
"I've had to put up with the Fake News from the first day I announced that I would be running for President".
The White House has been on the defensive since excerpts of the book were published last week with the president and his aides scrambling to discredit both its portrayal of Trump and the author's methods.
Mr Wolff's book, Fire and Fury: Inside the Trump White House, paints an unflattering portrait of Mr Trump, claiming the President's staff - and even his family members - regard him as "like a child".More news: Hoda Kotb Is Replacing Matt Lauer on the Today Show
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Tapper responded, "I have plenty of questions on immigration - you've attempted to filibuster by talking about your flights with the president".
"He delivers policy outcomes based on the information that we provide him", Pompeo said in a separate interview on CBS's "Face the Nation".
At Camp David this weekend, Trump "unloaded" on Bannon, a White House official said, and was greeted with praise by Senate Majority Leader Mitch McConnell, among others. Nikki Haley, the USA ambassador to the United Nations, also defended Trump's stability and said, "he didn't become the president by accident".
Miller replied that Bannon's role "has been greatly exaggerated, whereas the president hasn't gotten the due that he deserves".
"You have 24 hours of negative, anti-Trump, hysterical coverage on this network that led in recent weeks to some spectacularly embarrassing false reporting from your network", said Mr. Miller, the White House's senior advisor for policy.
Miller has appeared on the Sunday talk shows before to defend Trump. The entire interview can be seen in the second video.