Woodward, whose new book "Fear: Trump in the White House" hits book stores on Tuesday, described the incident in the interview with CBS as the most unsafe moment of Trump's nuclear standoff with North Korea.
During the same meeting Trump reportedly asked C Boyden Gray, former U.S. ambassador to the EU: "Which is going to be the next country to drop out [of the EU after Brexit]?"
In 2018 and 2020 the American people will get the chance to state clearly whose side they're on, Trump's or the subversive OP-ED writer, and I'll bet that the ideas and policies of Donald Trump win in both elections. The book claims that even after deleting the tweet, Trump raised the idea of evacuating military families from South Korea with Senator Lindsey Graham, who also told Trump that it was a unsafe idea.
Trump said if the person had a high-level security clearance, "I don't want him in those meetings".
U.S. President Donald Trump said on Friday he was open to sitting down with investigators probing possible collusion between his election campaign and Russian Federation "under certain circumstances", but did not want to get caught in a "perjury trap".
"People better wake up to what's going on", Woodward told "CBS Sunday Morning."
The first lady had a specific message for the author: "To the writer of the op-ed - you are not protecting this country, you are sabotaging it with your cowardly actions".
The op-ed came out the same week that details emerged from Washington Post reporter and editor Bob Woodward's new book, "Fear", about the atmosphere of chaos and dysfunction in the White House under Trump.
Pence said he did not know who wrote the Times column but that he was "100 percent confident that no one on the vice president's staff was involved in this anonymous editorial".
Trump was asked about the piece on Wednesday following an event at the White House.
House Speaker Paul Ryan took issue with the anonymous author of the op-ed, telling reporters that "a person who works in the administration serves at the pleasure of the president". In an interview with CNN's Christiane Amanpour, White House counsellor Kellyanne Conway said Trump believes the individual is someone from the national security sector of the government.
Others quickly followed suit to distance themselves from the Times op-ed, which claims there is an effort by a group of conservative administration insiders who are working against Trump.
What's the analog in the New York Times op-ed?
Gary Cohn, Trump's former top economic adviser who subsequently quit, by Woodward's account stole a letter off the president's desk to avoid him canceling a trade agreement with strategic ally South Korea.
Ryan also shrugged off any of the concerns expressed by the author as well as several other GOP lawmakers who have been critical of the president's fitness for office.
First lady Melania Trump also weighed in, praising the free press as "important to our democracy" before attacking the writer, saying "you are not protecting this country, you are sabotaging it with your cowardly actions".