Bush, then governor of Texas, indicated in the telephone conversation secretly taped by a friend that he had used the drug, but would not admit to it for fear of setting a bad example to children.
The tapes were recorded between 1998 and 2000 by author Doug Wead - a former aide to Bush's father George Bush Senior.
They were revealed on ABC Television News on Sunday and published by The New York Times newspaper.
To be president
Bush says on the tape: "I wouldn't answer the marijuana question. You know why? Because I don't want some little kid doing what I tried."
He added: "But you got to understand, I want to be president. I want to lead. Do you want your little kid say, 'Hey, Daddy, President Bush tried marijuana, I think I will'?"
"I wouldn't answer the marijuana question. You know why? Because I don't want some little kid doing what I tried"
US President George Bush
White House officials did not dispute the tapes' veracity and indicated the president was disappointed by their release.
"These were casual conversations that then governor Bush was having with someone he thought was a friend, and that's what they are," White House spokesman Scott McClellan told reporters travelling with Bush to Europe aboard Air Force One.
McClellan said Bush was unaware he was being recorded and the White House found out only when contacted by The New York Times for comment.
McClellan added that Bush had not been in contact with Wead for several years.
The author released portions of the tapes to coincide with the publication of his new book, and told ABC News he made the tapes because he believed the president was a historic figure.
"If I'd had a chance to tape record Gandhi or had conversations with Churchill, I probably would have recorded
them too," he said.
Means no harm
He also insisted his goal was not to hurt the president's credibility and said if this were the case he would have released the tapes during the 2004 election campaign.
Asked about the tapes in an interview with CNN, the president's father said he was not aware of them and declined to comment.
Bill Clinton infamously said he
smoked pot but did not inhale
Sitting next to Bush was former president Bill Clinton, who publicly admitted to smoking marijuana when he campaigned for the White House, but said he never inhaled the illegal drug.
The two former presidents are touring areas affected by the 26 December Indian Ocean tsunami.
In the tapes, Bush mocks then vice-president Al Gore for admitting to smoking the drug and dismisses him as "a pathological liar".