US Secretary of State Colin Powell has countered criticism that the Bush administration ignored the threat from al-Qaeda and Osama Bin Laden.
Powell said Bush had wanted to completely destroy al-Qaeda
Mr Powell was one of several top officials testifying before a commission looking into the 11 September 2001 attacks on America.
Mr Bush had pushed for a comprehensive strategy to destroy al-Qaeda, he said.
The hearings come after ex-White House counter-terrorism aide Richard Clarke criticised the Bush policy on terror.
Mr Clarke accused him of ignoring the threat from al-Qaeda - concentrating instead on Iraq.
In his first reaction to the criticism, Mr Bush said he would have taken faster action against al-Qaeda if he had had information before the 11 September attacks.
"Had my administration had any information that terrorists were going to attack New York City on 11 September, we would have acted," Mr Bush said.
Earlier, former Secretary of State Madelein Albright told the commission President Bill Clinton had done all he could to defeat al-Qaeda and Bin Laden.
Mrs Albright said Mr Clinton had authorised action to "neutralise" Bin Laden after the 1998 US embassy attacks in Africa - her worst day in office.
But despite those efforts, "we have failed to comprehend the gathering storm," former Defence Secretary William Cohen told the panel later.
"I believe we have been complacent," Mr Cohen said.
Mr Powell said the Bush team had been given extensive briefings on the threats posed by al-Qaeda and the Taleban by the outgoing Clinton administration, but not a counter-terrorism action plan.
Mr Bush, he said, had asked for a more aggressive approach than Mr Clinton's containment.
"I'm tired of swatting flies," Mr Powell quoted the president as saying.
"It was no longer to roll it [al-Qaeda] back, or reduce its effectiveness. Our goal was to destroy it," Mr Powell said.
Mr Powell said military action to destroy al-Qaeda - as well as any safe haven for terrorists by liberating Iraq - had not eliminated the terrorist threat against US targets.
"We know we have crippled their ability to work in Afghanistan, but we know they are trying to recreate themselves elsewhere. We've got to chase them."
Former counter-terrorism expert Mr Clarke is due to testify before the commission on Wednesday.
White House spokesman Scott McClellan has accused Mr Clarke of political opportunism ahead of November's presidential poll.
Vice-President Dick Cheney said that Mr Clarke clearly missed a lot of what was going on during his time at the White House.
The hearing will try to find whether any specific warnings were given
He also questioned Mr Clarke's effectiveness in running anti-terrorism efforts, citing the attacks on the US embassies in East Africa in 1998 and other incidents.
Mr Clarke served as head of counter-terrorism under four consecutive US presidents, from Ronald Reagan to George W Bush.
This is the eighth public hearing held by the bi-partisan commission, established in 2002.
The hearings - on Tuesday and Wednesday - are on "the formulation and conduct of US counter-terrorism policy".
ISSUES FOR COMMISSION
Congressional oversight and state of aviation security
Terrorism, al-Qaeda, and the Muslim world
Intelligence warnings against trans-national threats
Security and liberty
Border and aviation security
In a preliminary report on its findings so far, the commission said the Clinton and Bush administrations were too slow in moving away from diplomatic pressure to direct military action as a way of dealing with the al-Qaeda leadership.
In his opening statement, commission chairman Thomas Kean said he regretted that National Security Adviser Condoleezza Rice had declined to give evidence.
Defence Secretary Donald Rumsfeld and his predecessor William Cohen will also be testifying on Tuesday.
Mr Clinton's National Security Adviser Sandy Berger will testify on Wednesday as will Central Intelligence Agency Director George Tenet.