President George W Bush says he had a "wide-ranging and cordial" conversation with the commission investigating the 11 September 2001 attacks.
Bush and Cheney were questioned in the Oval Office
He and Vice-President Dick Cheney had answered all the questions asked during their joint appearance, Mr Bush said.
"I came away good about the session because I wanted them to know how I set strategy... how we deal with threats."
The two leaders were not under oath and no recording was made of the private session at the White House.
"I'm glad I did it. I'm glad I took the time... I enjoyed it," Mr Bush said after the conversation lasting more than three hours.
One member of the commission, Republican Jim Thompson, said the questions were addressed mainly to Mr Bush and none of them went unanswered.
"There was some laughter from time to time. The president is a bit of a tease," Mr Thompson told the Associated Press news agency.
"There were no tense moments. I thought the president gave a five-star performance. I wish the American people could have seen it."
Nothing to hide
Mr Bush was expected to be asked what he knew of the terrorism threat before the attacks and what action he took.
He did not say what the answer had been - but added that America continued to be vulnerable as al-Qaeda still existed and hated the US.
"I wanted them to know how I set strategy, how we run the White House, how we deal with threats," Mr Bush told reporters.
The meeting came after months of haggling between the White House and the commission over the ground rules for the president's appearance.
It was eventually agreed that the meeting would be held in the Oval Office, alongside Mr Cheney. There were no television cameras and also no photographs or transcripts of answers given by the two men.
Democrats had suggested the president's joint appearance with Mr Cheney might be an attempt to eliminate the possibility of providing contradictory testimony over whether the White House did all it could to head off the attacks.
But Mr Bush laughed off the suggestion.
"If I'd had anything to hide, I wouldn't have met them," Mr Bush told reporters outside the White House.
In a statement, the commission said they had found the president and his deputy "forthcoming and candid".
"The information they provided will be of great assistance to the Commission as it completes its final report," the statement said.
BUSH/CHENEY: LIKELY QUESTIONS
What they were told of the threat from terrorism in summer 2001
What action was taken against that threat
What action was taken on the day of the attacks
Whether military fighter jets were scrambled quickly enough
Why the president did not return to Washington straight away
Whether counter-terrorism efforts were neglected due to a fixation on Iraq
The 11 September attacks killed nearly 3,000 people after members of Osama Bin Laden's al-Qaeda network flew hijacked planes into New York's World Trade Center and the Pentagon.
Last month, Mr Bush's former counter-terrorism chief Richard Clarke alleged that fighting al-Qaeda was not as big a priority for the Bush administration as it was for his predecessor, Bill Clinton.
In April, a security memo presented to Mr Bush a month before the attacks and referring to al-Qaeda activity in the US was made public.
The White House had always maintained that it had no specific information that al-Qaeda was planning an attack inside the United States.
The commission - five Democrats and five Republicans - were expected to ask Mr Bush to provide evidence of what he had been told about the terror threat in the summer of 2001 and what actions he took, following Mr Clarke's testimony, experts say.
In particular, the panel is trying to establish whether the president acted quickly enough to give an order to military pilots, allowing them to bring down civilian aircraft on 11 September.
Previously, the highest official to testify to the commission was National Security Adviser Condoleezza Rice.
Ms Rice accepted there had been intelligence failings, but said there was "no silver bullet" that could have stopped the attacks, and the administration had done what it could.
Despite a polished performance, many commentators complained afterward she had left some key questions unanswered.
The president had been extensively briefed for his appearance by top White House officials, and his official lawyers were present during the Thursday meeting, where only note-taking was allowed.
"I was never advised by my counsel not to answer anything. I answered every question they asked," Mr Bush said.
"There was a lot of interest about how to better protect America," he said.
"They're very interested in the recommendations that they're going to lay out and I'm interested in that as well."
The commission is set to complete its final report in late July.