"They are mistaken," Mr. Bush said of the terrorists. "America will not retreat in the face of terrorists and murderers."
Mr. Bush came to the FBI training academy in Virginia to deliver a progress report on the war on terror. The White House said the address was planned before last week's bombings in London, but the deadly attacks give his remarks even more significance.
"There is only one course of action," the president said. "We will continue to take this fight to the enemy and we will fight until this enemy is defeated."
He spoke before an audience of 1,000 FBI officials, Marines and emergency first-responders. After his remarks, Mr. Bush went to shake hands with Attorney General Alberto Gonzales, who had been sitting in the front row. The handshake prompted a flurry of picture-taking since Gonzales is rumored as a candidate for the Supreme Court.
"Now why are you taking photos of us?" Bush playfully asked photographers. "One way to get in the paper is to stand next to Gonzales."
Mr. Bush's war against the terrorists is a major reason he won re-election last year: Americans came out of the voting booth saying they thought he would do a better job of protecting them from another attack.
It also remains his strength. Americans responded to an AP-Ipsos poll conducted last month by giving the president higher job approval ratings on terrorism than on his handling of the Iraq war, Social Security or other domestic issues.
Yet his approval numbers have slipped in recent months leading up to Monday's speech at Quantico.
"There will be tough fighting ahead," Mr. Bush cautioned. "There will be difficult moments along the path to victory. The terrorists know they can't defeat us on the battlefield. The only way the terrorists can win is if we lose our nerve. This isn't going to happen on my watch."
The president spoke at Quantico assaid it seems probable the London attacks were carried out by Islamic extremist terrorists.