Former President George W. Bush acknowledged he may have downplayed how much he sought advice from his father during his presidency, a sign of the influence George Herbert Walker Bush still has over his son.

It was a reminder that the father's legacy could have a powerful impact if another of his sons, Jeb Bush, wins the White House.

George W. Bush made the acknowledgement in a public forum Sunday, talking about his father's biography with the book's author, Jon Meacham.

During their conversation, Meacham recalled a conversation he'd had with George W. Bush for the book: "I think you downplayed at times how much you talked to your dad." The younger Bush nodded.

The forum at the George W. Bush Presidential Center in Dallas touched on the father's early career as a Navy pilot, his disappointing loss to former President Bill Clinton in 1992 and his reflections on his son's tenure in the White House. The talk came two days before Meacham's "Destiny and Power" becomes publicly available.

In the book, former President George H.W. Bush criticized his son for setting an abrasive tone on the world stage and failing to rein in hawkish Vice President Dick Cheney and Defense chief Donald Rumsfeld. That sensitive topic was not addressed in the Sunday forum where the younger Bush was asking the questions.

The biography is the fullest account yet of the elder Bush, the only modern ex-president not to write a full-length memoir. It draws on diaries Bush kept from the 1960s to the 1990s and interviews the author conducted from 2006-2015.

On some days he sounded like he was "a step away from the grave," Meacham said, referring to the exhaustive schedule kept by Bush. Meacham praised the elder Bush for his candor in recording his own history.

"This is a man who turned on the tape recorder and told the truth. Even when he was having the worst possible day he would talk himself back into the game," Meacham added, citing Bush's discouraged but determined diary entry on the evening he lost his bid for a second term as president.

In the book, Meacham portrays the 41st president as the epitome of gentility and grace, bred for power but also humbled by it. In contrast to Ronald Reagan, for whom Bush served eight years as vice president, or Richard Nixon, whose patronage he enjoyed, Meacham said Sunday that Bush saw politics as a noble undertaking, in the mold of Theodore Roosevelt and Franklin Delano Roosevelt, "where public office was an extension of yourself."

In 1965, after losing an election to the U.S. Senate, Bush, at 41 years old, declared his intention to become president.

"He had a sense of destiny, a sense that he was meant to do great things," Meacham said, adding that his father and in-laws had both predicted his rise to the White House.

"When you write the book on me, you're not going to find anyone predicting I'm going to be president," Bush quipped.

Toward the end of the discussion, Bush and Meacham turned to former President George H.W. Bush's reflections on his son's presidency.

In the book, Bush says Rumsfeld "served the president badly" when George W. Bush was in the White House and that former Cheney "built his own empire" and asserted too much "hard-line" influence.

He worried about his son's "cowboy image," Meacham writes.

"I do worry about some of the rhetoric that was out there -- some of it his, maybe, and some of it the people around him," Bush said in the book.

Bush disliked the term "axis of evil," which George W. Bush used to refer to Iraq, Iran and North Korea in his 2002 State of the Union address.

During his son's years in office, George H.W. Bush devoured the news.

"There's another difference, I didn't read The New York Times," George W. Bush told Meacham with a chuckle.

The elder Bush was a far more emotional person than the image he presented publicly, Meacham said.

Criticized during his presidency for raising taxes after pledging as a candidate, "Read my lips: no new taxes," George H.W. Bush consistently put the country's interests ahead of his own, Meacham said. That pledge enraged many conservatives in his own party.