"The terrorists will continue their missions of murder and suicide until they are stopped. And we will stop them," Mr. Bush told a joint session of the Philippine Congress.
He and Philippine President Gloria Macapagal Arroyo agreed to beef up their military cooperation, including intensifying an already existing partnership to boost mixed efforts to defeat al Qaeda-linked militant extremist groups that operate in the islands.
Arroyo was grateful to Mr. Bush for American security assistance. "We must close ranks and stand firm against terrorist threats, however grave," she said as the two appeared together before reporters.
Mr. Bush's visit was an abbreviated one - only eight hours for talks with Arroyo, the speech to Congress and a formal state dinner - due to concerns about potential terrorist activity. Mr. Bush then flew to Thailand and was spending the night there.
CBS News Correspondent Mark Knoller says the stop in Thailand was to be the longest of the president's trip. He was to spend the better part of three days there. First, Mr. Bush was to make a state visit -- then he was to attend the annual Asia-Pacific Economic Summit -- where he's looking for more support in the war on terror -- and in securing and rebuilding Iraq -- and for Thailand's help.
Mr. Bush's brief stay in the Philippines was the second stop on a six-nation tour of Asia and Australia.
On its way into Manila, Air Force One was escorted by a pair of U.S. fighter jets that flew so close the pilots' faces were clearly visible from the presidential aircraft.
And the president's speech before the Congress was delayed nearly an hour because of concerns about large crowds - both supporters and protesters - on his motorcade route.
White House press secretary Scott McClellan said people had to be moved back to address Secret Service worries about "safety issues." U.S. officials privately said demonstrators on or near the motorcade route posed the biggest problem.
What remained for Mr. Bush to see along the route from Malacanang Palace to the speech were mostly thousands of well-wishers.
But about 3,000 protesters had marched through the city to position themselves near the House of Representatives building, the site of Mr. Bush's address. They burned Mr. Bush in effigy and five flags as the motorcade passed.
Seven legislators walked out of the hall at the start of Mr. Bush's speech, after plans for a larger walkout fizzled.
The president gave no sign he had noticed them or the demonstrators. Instead, he singled out for thanks all those who "lined the streets" in welcome. "It warmed our hearts," he told the Congress.
During an earlier picture-taking session with Arroyo, the president praised the Philippine leader's anti-terror fight, and said the threat here from the al Qaeda-linked Abu Sayyaf Muslim extremist group was particularly dangerous.
"It's serious because there are no rules when it comes to a crowd like Abu Sayyaf - they kidnap, they kill, they maim," Mr. Bush told reporters. He called Arroyo a "strong and stalwart leader."
Mr. Bush, pointing to the recent killing of an Abu Sayyaf leader and the capture of others, told reporters that "the success against this particular group is a model for the region."
In talks that lasted about an hour, Mr. Bush told Arroyo "we will do what we can to assist" in modernizing the Philippine army, said a senior administration official who briefed reporters on the session.
That will include delivery of 20 refurbished Huey military helicopters, said the official, who spoke on the condition of anonymity.
The official said the U.S. contribution would be mostly in the forms of advisers and technical assistance, the kind of help the United States has already been providing, and that the pricetag had yet to be determined. The Philippine government itself was expected to come up with "hundreds of millions" of dollars, the official said.
Toasting her state dinner guest - who wore a traditional Philippine barong open-necked shirt for the evening festivities - Arroyo said the U.S.-Philippine "relationship has ripened."
Meanwhile, the official confirmed news reports that Mr. Bush in Bangkok would announce he's upgrading U.S. military ties with Thailand, designating it a "major non-NATO ally." That status will allow the United States to provide more advanced military equipment.
Mr. Bush himself signaled the upgrade, saying in an interview with Nation TV of Thailand, "We have a common interest to make sure our countries are secure." The Philippines was also recently granted such a status.
The first U.S. president to address the Philippine Congress since Dwight Eisenhower in 1960, Mr. Bush thanked the country for its early support of U.S. policy in Iraq. The Philippines has sent about 100 soldiers, police and health workers to Iraq.
Turning to the countries' cooperation in the war on terror, Mr. Bush referred to the Sept. 11, 2001, terror attacks in the United States and what he called "bombings and kidnappings and brutal murders of the innocent" in the Philippines to say that both countries have "seen the enemy on our own soil."