Condoleezza Rice has appeared before an official inquiry to respond to criticism that Bush underestimated the threat posed by the group before the 11 September 2001 attacks on Washington and New York.
"President Bush understood the threat, and he understood its importance," she said in her opening statement on Thursday.
"He made clear to us that he did not want to respond to al-Qaida one attack at a time. He told me he was 'tired of swatting flies'."
Rice calmly admitted there were indications in the summer of 2001 that suspected al-Qaida operatives were planning a major attack against US interests.
"Yet, as your hearings have shown, there was no silver bullet that could have prevented the 9/11 attacks,'' she told the commission headed by Thomas Kean, former Republican governor of New Jersey, and Lee Hamilton, a former Democratic congressman from Indiana.
Rice, under oath and before a live national television audience, clashed with Democratic members of the bipartisan commission over whether the Bush administration was negligent in the summer before the hijacked airliner attacks.
Bush was told Usama bin Ladin
was determined to attack the US
"The terrorists were at war with us, but we were not yet at war with them. For more than 20 years, the terrorist threat gathered, and America's response across several administrations of both parties was insufficient," Rice said.
Commissioner Richard Ben-Veniste, a Democrat, pressed Rice on a briefing given to Bush on 6 August 2001, when a document was presented entitled: Bin Ladin Determined to Attack Inside the United States.
As members of the audience, including some family members of 9/11 victims applauded, Ben-Veniste demanded the report should be declassified. Rice revealed the title, but said it contained no specific threats.
Bush, who first opposed the creation of the commission and later picked its members, initially refused to subject Rice to a public hearing, arguing this would compromise the constitutional separation of powers.
But damaging accusations from former White House counter-terrorism chief Richard Clarke late last month - that the administration did not take the threat from al-Qaida seriously and was obsessed with toppling Saddam Hussein - forced Bush to change his stance last week.
Clarke's allegations have been backed by former Treasury Secretary Paul O'Neill.
Rice did not mention Clarke's claims, but described him as having worked closely with the White House to develop a comprehensive antiterrorism policy and to activate measures that had lain dormant.