"The things — some of the things — that Trump did and does jeopardizes the real national security," said Woodward, who has written books about several administrations and helped to break the Watergate scandal that brought down President Richard Nixon.
The White House didn't immediately respond to questions about Woodward's remarks.
Woodward's book and the Times op-ed highlighted instances of high-ranking officials — in one example ripping papers off the president's desk to prevent a policy move — trying to subvert what they consider the president's worst impulses. As the revelations reverberate in Washington and around the country, they show a Republican Party and financial community largely unperturbed by Trump's temperament — at least as long as the economy and corporate profits stay strong.
Stocks may continue their steady rise. Most GOP lawmakers will likely defend the president as more stories about chaos surface. But what may decide Trump's political fate is whether the independent and GOP voters who will help to determine the swing races in November's battle for Congress care about the risks posed by Trump's presidency.
On Monday morning, Trump himself claimed Woodward used his book — which comes out Tuesday — to help Democrats. Pointing to Cabinet members' denials of explosive quotes attributed to them, Trump tweeted that the journalist "is like a Dem operative prior to the midterms."
No evidence supports the president's contention that Woodward is trying to help Democrats, who appear to be at least slight favorites to take a House majority in the next Congress. Control of the chamber would notably allow Democrats to start investigations into the administration, or potentially push for Trump's impeachment.
In a series of tweets Monday, the president tried to deflect attention from Woodward's book. The U.S. economy "is soooo good" that "Democrats are flailing & lying" with "phony books, articles and T.V. 'hits' like no other [politician] has had to endure," the president tweeted.
"And they are losing big," he added.
Notable Republicans, with only a few exceptions, have also shown little public concern about the episodes outlined in Woodward's book. They have instead focused on selling a strong U.S. economy and the positive boost they say last year's GOP tax overhaul and an emphasis on deregulation have provided.
"I know the president is very unconventional, and I know his tweeting and unconventional tactics bother people," House Speaker Paul Ryan told reporters last week after the Times op-ed was published. But the Wisconsin Republican said that "our branch of government is in charge of making sure that we pass good laws that improve people's lives."
"And guess what, we are passing good laws that improve people's lives," added Ryan, who is not seeking another term this fall.
Sen. Lindsey Graham, R-S.C., expressed a similar sentiment when responding to former President Barack Obama's criticism of Trump's temperament and his effect on the country's discourse. In a tweet, he contended that voters "wanted a better way" than the path the Democratic president offered.
"The Obama years were dominated by higher taxes, slower growth, big government, a broken military, and a pathetically weak foreign policy," he tweeted Friday.
Some Republicans have at least occasionally criticized the president and continued to do so after excerpts of Woodward's book started circulating. Sen. Bob Corker, a Tennessee Republican who once described the White House as an "adult day care center," said last week that the Times column did not shock him.
"I don't think those of us who have worked closely with people in the White House are shocked by the content," Corker, who will retire in January, said in a statement.