Manila, Philippines ? The Philippine military stepped up its attack Sunday on Muslim rebels considered more vulnerable now that they no longer hold hostages as human shields.

The military said that up to 1,800 more troops were joining forces that began attacking the Abu Sayyaf guerrillas in the jungles of three southern islands.

“We’re now operating with greater intensity,” said Maj. Gen. Ernesto Carolina, head of southern Philippine forces. “We will not let them get away with this.”

The new offensive began after troops ambushed the rebels Friday on the main southern Philippine island of Mindanao. Two hostages died during a gun battle: Filipina nurse Ediborah Yap, 45, and 42-year-old missionary Martin Burnham of Wichita, Kan.

Burnham’s wife, Gracia, survived the fighting with a bullet wound in her thigh.

Carolina said the rebels were more vulnerable now that they had no hostages. But he said the army was still reluctant to bomb them from the air for fear of hitting pursuing troops.

The three-pronged operation was focusing on the mountainous, jungle-covered islands of Jolo, Basilan and Mindanao. The area is in a 60-mile stretch of the Sulu Sea in the extreme southwest of the Philippines.

On Mindanao, soldiers were hunting Abu Sayyaf leader Abu Sabaya, who fled into dense jungle with about 40 men after the army attacked them in Friday’s rescue mission. The group has been linked to the international al-Qaida terror network.

Other troops were hunting commander Isnilon Hapilon on Basilan. On Jolo, they were stalking Khaddafy Janjalani, another rebel leader.

“If we get the three, the others will fall,” Carolina said.

The Abu Sayyaf forces on Basilan and Mindanao are thought to number less than 100 fighters, down from more than 1,000 a year ago, after steady army attacks. Several hundred more fighters may still inhabit Jolo island.

U.S. Ambassador Francis Ricciardone would not say if bullets fired by rebels or Philippine forces killed Martin Burnham. That issue was irrelevant, he said, because the rebels were ultimately responsible for the death of a man who should not have been held so long.

The ambassador said Washington had no plans to do a formal investigation about whether the rescue mission was executed properly.

“No one should try to suggest this was bungled or botched in any way,” Ricciardone said, adding that the mission could not have been a textbook operation because it took place in dense jungle and pouring rain.