Philippine troops closed in Thursday on another veteran of the Abu Sayyaf extremist group, a day after announcing the death of a senior leader wanted in the beheading of a California tourist.

Encouraged by the death of Abu Sulaiman, President Gloria Macapagal Arroyo vowed to finish off the Islamic militants "with a hand of steel" and U.S. assistance.

Sulaiman, 41, whose real name was Jainal Antel Sali Jr., left a legacy of lethal attacks and kidnappings, putting him on U.S. and Philippine most-wanted lists. The U.S. had offered up to $5 million for his capture or killing.

After years of tracking Sulaiman, U.S.-backed Philippine troops cornered him and other rebel leaders Tuesday in a Jolo island jungle hide-out about 600 miles south of Manila. He died in the ensuing gunbattle, military officials said.

On Thursday, a Philippine Marines platoon battled about 30 extremists under Abu Sayyaf veteran Radullan Sahiron in the Jolo town of Patikul, said Marine spokesman Lt. Col. Ariel Caculitan.

Ten Abu Sayyaf members and three government troops died in the hour-long fight, while three militants were captured. Caculitan said officials have yet to identify those killed or captured, and to ascertain if Sahiron was among them.

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The U.S. has offered a $200,000 reward for Sahiron's capture or killing.

Arroyo said the "relentless pressure" on the militants "is taking its toll, and we will keep it up until all the terrorists and their clandestine cells are accounted for."

"This government is determined to finish the job with a hand of steel against evil," Arroyo said at a meeting with U.S. Ambassador Kristie Kenney and military and defense officials. U.S. troops and military advisers in the southern Philippines have provided training and intelligence for the four-month-long offensive.

Kenney congratulated the military on "capturing some of the world's most deadly terrorists."

Sulaiman had claimed responsibility for a 2004 bombing aboard a Philippine ferry. The blast and resulting fire killed 116 people in Southeast Asia's second-worst terror attack.

He was perhaps best known in the U.S. for plotting the kidnapping of American and Filipino tourists from a resort on the southeastern island of Palawan in 2001. One of the Americans, Guillermo Sobero, was beheaded.

Gracia Burnham, another of the hostages, said in a statement Wednesday that Sulaiman now faces God's judgment.

"Based on the six months I had close contact with Sulaiman during our year of captivity, I would say he was the most dangerous of the Abu Sayyaf leaders because he was filled with hate," she said.

Burnham and her husband, Martin, both missionaries, were held for more than a year. She was wounded and her husband died in the rescue effort that freed her.

The kidnappings prompted Philippine authorities to allow the deployment of U.S. troops in the southern Mindanao region to train and arm Filipino soldiers working to wipe out Abu Sayyaf.

Two soldiers were killed in the three-hour gunbattle at Sulaiman's camp, which was fortified with 17 bunkers and resembled a bomb factory, regional army spokesman Maj. Eugene Batara said. Other insurgents escaped and troops pursued them, Batara said.

The battle involved the army's 8th Special Forces Company and about 60 Abu Sayyaf gunmen, military chief Gen. Hermogenes Esperon told reporters.

Two top Indonesian terror suspects — Omar Patek and a man known as Dulmatin — were believed to be hiding in the camp, the military said. Both are blamed for the 2002 Bali bombings that killed 202 people in Indonesia.

Philippine special forces photographed and buried the only body recovered from the rebel compound, not realizing that it was Sulaiman, Esperon said. It was later exhumed and Jolo villagers, a rebel informant and one of Sulaiman's wives identified the remains, Esperon said.

Esperon described the rebel leader — a former civil engineer — as the highest-ranking Abu Sayyaf commander killed by U.S.-backed troops.

Aside from the ferry attack and the kidnappings, Sulaiman also had a hand in a bombing that killed a U.S. serviceman in 2002, the military chief said.