Woodward, who has covered every administration since his groundbreaking coverage of President Richard Nixon and the Watergate scandal, said yes.
Other Trump aides, including chief of staff John Kelly and Defense Secretary James Mattis, have denied quotes attributed to them in the book - quotes that ridicule Trump as "unhinged" and acting like a grade-school child.
The 75-year-old Woodward said that at a National Security Council meeting a year into Trump's presidency, when he was complaining about the cost of posting thousands of USA troops in foreign countries, Secretary of Defense Jim Mattis had to explain the rationale to him.
"I don't think there's any one author", he told Fox News host Laura Ingraham on "The Ingraham Angle".
However, giving his reaction on the book which was released on Tuesday, Donald Trump said that Woodward book is scam and he did not speak in the way he has been quoted. He said people in Trump's administration are anxious that the president will sign things or give orders that threaten USA or world security and finances.
The book has already risen to No. 1 on Amazon's best-seller list, but Trump said Woodward used "now disproven unnamed and anonymous sources". According to Woodward, Trump made this comment during a Situation Room meeting in the White House on July 19 previous year, almost three weeks after he had a very successful meeting with Modi at the White House on June 26. The book describes moments when staff members joined together to purposefully block what they believe are the president's most risky impulses - sometimes by surreptitiously removing papers from the president's desk.
US southeast braces for 'days and days' of floods from hurricane
Isaac became a tropical storm again approaching the Caribbean, while Hurricane Helene was veering northward, no threat to land. ET (0900 GMT), according to the NHC, which warned it would be "an extremely unsafe major hurricane" through Thursday night.
But neither Cohn nor Porter said specifically what was inaccurate, and neither denied speaking to Woodward. And that's what we got to do.
"Doing everything I can", Pence told Cohn, according to the book. Fulfilling this responsibility does not make someone part of a "resistance" or mean they are seeking to "thwart" the President's agenda.
Bannon called the piece "absolutely outrageous" and encouraged the Trump administration to figure out the people responsible for it.
I knew that people in office in these sensitive positions were not going to talk on the record. But Woodward found himself reprising the reporting tactics he deployed at the start of his career, before he was the nation's most famous investigative reporter and the author now of 19 books.
Nevertheless, Woodward continues to float the idea they are "saving the country".
Woodward insisted he doesn't take a side in that debate.
The book claims that Trump falsely suggested that McCain took an early-release from the PoW camp in Vietnam-something that Mattis quickly told the President wasn't true.