One soldier was also wounded in the fighting in a village in Patikul town on Jolo island, 1,000 kilometres south of Manila, on Thursday, said Brigadier General Cirilito Sobejana, commander of an anti-terrorism task force.
The hostages were not rescued, and pursuit operations were ongoing, Sobejana said.
The construction workers were abducted on July 15 from a school in Patikul by suspected members of the Abu Sayyaf terrorist group, which had demanded 1 million pesos (20,000 dollars) for each of the hostages.
Aside from the construction workers, the Abu Sayyaf is still holding captive about 20 hostages, including 14 foreigners, in Jolo and Basilan.
The terrorists beheaded two Vietnamese hostages earlier in the month, while another Vietnamese captive was killed during a clash between his captors and government troops last week.
The Abu Sayyaf is one of the most active militant groups in the southern Philippines, and is believed to be allied with the Islamic State terrorist organization.
One of the Abu Sayyaf's leaders, Isnilon Hapilon, has been identified as the head of Islamic State-allied militants currently fighting government troops in besieged Marawi City, 800 kilometres south of Manila.
The conflict in Marawi has left more than 600 people dead, including nearly 100 government forces and 421 militants. Forty-five civilians have been executed by the terrorists while 40 displaced residents have died from illness.
The Abu Sayyaf is one of the most active militant groups in the southern Philippines
Two suspected Abu Sayyaf terrorists were killed in a firefight with government troops in the southern Philippines during a rescue operation for four construction workers abducted last week, the military said on Friday.
