"We will not rest, we will not retreat, we will not withdraw from the fight until this threat to civilization is removed," Bush told a gathering of the Military Officers Association of America.
The president said Al Qaeda is "convinced they can force America to retreat… that we are weak and decadent and lacking in patience and resolve and they're wrong."
Bush warned that allowing Al Qaeda to gain a foothold in Iraq would doom security in the region and around the world.
"They oppose the advance of freedom, and they want to gain control of weapons of mass destruction," he said. "If they drive the forces of freedom out of the region, they will have an open field to pursue their dangerous goals."
Usama Bin Laden was singled out by the president as the focus of center of terrorism.
Bush said the architect of the 9/11 attacks was actively trying to a execute plan to gain control of the country, including a plan to create a "unit responsible for arrests, murder and destruction."
Bush vowed the United States would do whatever it takes to keep "the most dangerous men from getting their hands on the world's most dangerous weapons.
"The best way to protect America is to stay on the offense," he said.
Bush's speech, the latest in a series that began last week to bolster the administration's Iraq and Afghanistan strategies, also came hours after the release of status report in the War on Terror.
The White House report said: "The United States and our partners continue to pursue a significantly degraded but still dangerous Al Qaeda network."
"Yet the enemy we face today in the war on terror is not the same enemy we faced on Sept. 11," said the 23-page terrorism strategy update. "Our effective counterterrorist efforts in part have forced the terrorists to evolve and modify their ways of doing business."
Two months before the midterm elections, the report was the White House's latest attempt to highlight national security, an issue that has helped Republicans in past campaigns. Democrats were releasing their own assessment.
Democrats released their own study, saying it shows the country is less secure today than before Bush took office. Citing research done by the nonpartisan, nonprofit Memorial Institute for the Prevention of Terrorism, the report said the number of Al Qaeda members has jumped from 20,000 in 2001 to 50,000 today. It also charged that average weekly attacks in Iraq have jumped from almost 200 in spring 2004 to more than 600 this year, using numbers provided by the liberal-oriented Brookings Institution think tank.
"All the speeches in the world won't change what's going on in Iraq," said Senate Minority Leader Harry Reid.
"The truth is the president's policies have not worked and have not made us safer," said Sen. Thomas R. Carper, D-Del.
The updated White House strategy came in the wake of the release of a new Al Qaeda video over the weekend that raised concerns about the possibility of another attack as the fifth anniversary of Sept. 11 approaches. The tape featured an American — believed by the FBI to have attended Al Qaeda training camps — calling for his countrymen to convert to Islam.
Asked about this Tuesday, Fran Townsend, a special assistant to President Bush for homeland security and counterterrorism, said she did not think the tape suggested another strike.
"We've seen tapes before. We've seen these sort of releases right near Sept. 11," she said on ABC's "Good Morning America."
"There are no plans to raise the threat (terror) threat level," Townsend said.
The Department of Homeland Security had raised the terror threat for aviation to red — its highest level — in mid-August at the time the British, working with the United States, broke up what was purported to be a plot against international flights bound from Britain to the United States.
The administration's Iraq war policy and terrorism strategy have come under increasing criticism in recent months, and Republicans and Democrats returning to Capitol Hill Tuesday for the fall season were set to debate the strategy as the midterm elections draw near.
Five years after the attacks on the World Trade Center in New York and the Pentagon, about a third of the American people think the terrorists are winning, according to a recent AP-Ipsos poll.
In its updated terror-fighting strategy, the administration took credit for some successes, saying that "we have deprived Al Qaeda of safe haven in Afghanistan and helped a democratic government rise in its place. It also said that "a multinational coalition joined by the Iraqis is aggressively prosecuting the war against the terrorists in Iraq."
But it also acknowledged continuing challenges:
—"Terrorist networks today are more dispersed and less centralized. They are more reliant on smaller cells inspired by a common ideology and less directed by a central command structure."
—"While the United States government and its partners have thwarted many attacks, we have not been able to prevent them all. Terrorists have struck in many places throughout the world, from Bali to Beslan to Baghdad."
—"While we have substantially improved our air, land, sea and border security, our Homeland is not immune from attack."
—"The ongoing fight for freedom in Iraq has been twisted by terrorist propaganda as a rallying cry."
Bush has said on many occasions that the country must be prepared for a drawn-out battle against a new kind of enemy, and the new counterterrorism strategy released Tuesday says flatly that "the War on Terror will be a long war."
It says that among the strategies the United States must emphasize are making all sovereign nations accountable for what happens on their soil, strengthening existing coalitions and partnerships against terrorists and continue to develop more expertise in this area.
One particular problem, it noted, is an "increasingly sophisticated use of the Internet and media" by terrorists and would-be terrorists, saying these tactics have allowed enemies of the United States to "rally support, proselytize and spread their propaganda without risking personal contact."
It also maintains that terrorism "is not simply a result of hostility to U.S. policy in Iraq."
"The United States was attacked on September 11 and many years earlier, well before we toppled the Saddam Hussein regime," it said. "Moreover, countries that did not participate in coalition efforts in Iraq have not been spared from terror attacks."
"There will continue to be challenges ahead, but along with our partners, we will attack terrorism and its ideology and bring hope and freedom to the people of the world," the policy statement said.
"This is how we will win the War on Terror."
FOX News' Wendell Goler and The Associated Press contributed to this report.