Bob Woodward appeared on the "Today" show Monday morning to discuss "Fear," his new book on the Trump administration.

In the new book, Woodward quotes chief of staff John Kelly as calling President Donald Trump an "idiot," while Secretary of Defense James Mattis allegedly said Trump was like "a fifth or sixth grader."

Both Kelly and Mattis have denied the quotes.

When asked about their denials, Woodward said: "They are not telling the truth."

Bob Woodward said White House chief of staff John Kelly and Secretary of Defense James Mattis are "not telling the truth" after they denied quotes attributed to them in the veteran journalist's new book, "Fear."

The book, which comes out Tuesday, gives a new look into the inner workings of President Donald Trump's White House. In the book, which has been previewed by The Washington Post, Kelly is said to have called the president an "idiot," while Mattis reportedly compared Trump's intellect to that of a "fifth or sixth grader."

During an interview on the "Today" show Monday morning, co-host Savannah Guthrie asked Woodward if Kelly and Mattis were "lying" when they denied their portrayals in his book.

"They are not telling the truth," Woodward said.

He added: 'These are political statements to protect their jobs, totally understandable."

Secretary of Defense James Mattis (left) and White House Chief of Staff John Kelly (right) have both denied their depictions in Woodward's book. AP

"Have you ever done one of these books, know you talked to a source and the source comes out publicly after the publication and says, 'That's not true,'" Guthrie asked.

"It happens frequently," Woodward said.

When asked if it happened with this book, Woodward refused to answer, saying he wants to focus on Trump's actions.

"Some of the things Trump did, and does, jeopardize the real national security," Woodward said.

For example, he said that the president imposing tariffs goes against what "99.9%" of experts have recommended.

"It doesn't work. He's got it in his head, when people challenge him, he'll say, 'Oh, I've had those ideas for 30 years. You're wrong,'" Woodward said.

Woodward, who was one of the two journalists to uncover the Watergate scandal, said that he's "never seen an instance when the president is so detached from the reality of what's going on."

He gives one example of a National Security Council meeting that happened about a year after Trump took the White House. At the meeting, Trump reportedly began to complain about "all this money we're spending on US forces abroad," and Mattis had to explain why it was necessary.

"Mattis says to him, 'We're doing this to prevent World War III,'" Woodward said.

He said Mattis went on to say that "If we don't keep these programs ... the only deterrent option we have will be the nuclear option."

The White House last week called Woodward's new book "nothing more than fabricated stories."

Trump himself took to Twitter to decry the exposé, saying it was a "scam." At a rally last week, he also called Woodward an "idiot."

Following Woodward's appearance on the "Today" show, Trump took to Twitter and said, "Woodward is a liar who is like a Dem operative prior to the Midterms. He was caught cold, even by NBC."

Watch Woodward's full interview below: