Former US president Richard Nixon lied in 1972 about the true impact of the aerial bombing of Vietnam to advance his re-election prospects, a new book by Bob Woodward says, citing a previously unpublished presidential note.

Nixon scribbled the note sideways across a top-secret memo from his national security adviser, Henry Kissinger.

"K. We've had 10 years of total control of the air over Laos and V.Nam. The result = Zilch. There is something wrong with the strategy or the Air Force," he wrote.

Woodward noted that just the day before, Nixon had asserted in an hour-long interview with Dan Rather of CBS News that the bombing had been "very, very effective."

The claim was "a lie, and here Nixon made clear that he knew it," writes Woodward in "The Last of the President's Men," arguing that Nixon defended and intensified the bombing anyway to advance his re-election prospects, according to the Washington Post, which had access to the book.

Woodward, with fellow Washington Post reporter Carl Bernstein, exposed the Watergate scandal, which ultimately led to Nixon's resignation in 1974.

What began as a burglary of the Democratic National Committee headquarters at the Watergate hotel escalated into a cover-up directed by Nixon, much of it captured on a secret White House taping system.

In his new book, Woodward draws from previously unpublished documents and many hours of interviews with Alexander Butterfield, a former top White House aide who disclosed the existence of the taping system to Senate investigators, sealing Nixon's fate.

When he left the White House, Butterfield, now 89, took with him thousands of confidential documents detailing Nixon's 1969-1974 presidency, according to the book.

"I just took my boxes of stuff and left," Butterfield is quoted as saying, acknowledging it was improper to have taken them and promising to deposit them with an appropriate archive.

Nixon, the 37th US president, died in April 1994 at age 81.