Trump has taken aim at the Woodward book, repeatedly slamming it as "fiction" and "a scam" on Twitter.
Cohn did not detail his complaints with the book, telling Axios: "I am proud of my service in the Trump Administration, and I continue to support the President and his economic agenda".
During the meeting, according to Woodward's book, Trump said: "Pakistan isn't helping us".
But neither Cohn nor Porter said specifically what was inaccurate, and neither denied speaking to Woodward. The US, Trump said, "must stop making payments to Pakistan until they cooperate".
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On Wednesday, former New Jersey Governor Chris Christie accused former White House chief strategist Stephen Bannon of being the "co-author" to journalist Bob Woodward's anti-Trump book, "Fear: Trump in the White House".
"Trump in the White House", made some astounding revelations and painted a picture of a chaotic White House, with aides at their wit's end with the commander-in-chief.
The president blasted Brzezinski as "low I.Q. Crazy Mika" and said she had been "bleeding badly from a face-lift" during a New Year's party at his Florida resort.
The op-ed was not the only thing on Trump's mind as he called around to advisers over the weekend, according to two people familiar with the conversations.
Nothing of significance has emerged from the efforts to exploit Afghanistan's minerals, but Trump's Afghanistan-centric South Asia strategy, unveiled in August 2017, said the USA would stay with additional troops.
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"Just run the presses - print money", Trump said, according to Woodward, during a discussion on the national debt with Gary Cohn, former director of the White House National Economic Council.
White House press secretary Sarah Sanders assured reporters Monday that the president is not now considering using lie detectors to figure out which senior administrative official wrote the anonymous op-ed, The Washington Examiner reported.
In his first of what promises to be an exhaustive round of media interviews, the noted journalist who, along with Carl Bernstein, won the Pulitzer Prize for coverage of Watergate, told David Martin of CBS News, "You look at the operation of this White House and you have to say, Let's hope to God we don't have a crisis".
"One key person who's in office called me and said, "Everyone knows what you said here is true".
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"Well, the book is already out", he said.