Col. Francisco Gudani said his men while fighting could see the Abu Sayyaf rebels holding Wichita, Kansas, missionaries Martin and Gracia Burnham on the southern island of Basilan.
At least 11 guerrillas were killed and two soldiers were wounded in the fighting, military officials said.
Â"There is heavy fighting right now in Basilan and we have visual contact with the enemies,Â" Gudani said. Â"The Burnham couple are with the gunmen whom soldiers are now fighting in the hinterlands.Â"
The Abu Sayyaf rebels hold at least 10 Filipino hostages, mostly workers seized from coconut plantations, but the military did not know if any of them were with the unit attacked Tuesday.
The fighting comes a day after the Abu Sayyaf threatened to behead the Burnhams if the military does not stop its assault.
Gudani said the Abu Sayyaf are under increasing pressure.
Â"They are short of ammunition...They have little food and are hungry and they lack the necessary rest. It's only a matter of time before we can get them,Â" Gudani said.
The Abu Sayyaf, thought to number 1,000 fighters, has kidnapped dozens of foreigners and Filipinos in recent years and raised millions of dollars in ransom.
The group, which has beheaded several hostages, has suspected links to Osama bin Laden, the Saudi exile accused of plotting the Sept. 11 terrorist attacks in the United States.
Gudani cited no immediate reports of casualties and issued a radio appeal for the guerrillas to surrender.
Â"To the Abu Sayyaf, listen to this...surrender peacefully and we guarantee that no harm will come your way,Â" Gudani told the Radio Mindanao Network.
He said the fighting is near Lantawan town, about 10 kilometers (six miles) south of the Basilan provincial capital of Lantawan and 900 kilometers (560 miles) south of Manila.
The Burnhams, along with Peruvian-American Guillermo Sobero, of Corona, California, and 17 Filipinos, were taken hostage from a southwestern beach resort on May 27.
The guerrillas and hostages were first surrounded in early June when they invaded a hospital on Basilan island to take doctors and medical supplies. But they escaped under cover of darkness, prompting a Senate inquiry into how they fled. The guerrillas escaped similar assaults in the past.
A man put on line by rebels during a telephone interview on Monday, identified as Martin Burnham, told RMN he was Â"very tired, weak and scared.Â"
He appealed to the government to halt its attack.
Â"The artillery and the airstrikes are very frightening because they were so random. They cannot rescue me with artillery,Â" he said.
The skeletal remains of Sobero were found more than a week ago on Basilan, ending speculation that he may be alive despite the guerrillas' claim they beheaded him in June.
The United States is helping the Phiippines train and supply weapons to some of the more than 7,000 Filipino soldiers pursuing the Abu Sayyaf.
The guerrillas claim to be fighting for Muslim independence in the southern Philippines, but the government dismisses them as mere bandits.
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