Residents of Butig, which has a population of 17,000, have fled after the IS-linked militants holed themselves up in an abandoned government building, Philippine military spokesman Brigadier-General Restituto Padilla said.
"The Armed Forces of the Philippines has launched an operation to chase after the Maute leaders," Padilla told AFP, adding that artillery and military aircraft were aiding ground-based security forces.
Two soldiers had been wounded in skirmishes with the Maute group since military operations began on Thursday, he said.
The stand-off follows the arrest of three members of the group last month, accused of the September bombing that left 15 people dead in Davao, Duterte's hometown and Mindanao's largest city.
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Government forces have surrounded between 50-100 Maute gunmen to prevent a possible spillover of the fighting to other areas, Major Filemon Tan, the military spokesman for the southern Philippines, told ABS-CBN television.
He did not provide details of troop numbers.
Butig is a mainly Muslim rural town on the lower slopes of Ragang, one of the country's tallest mountains and more than 800 kilometres south of Manila.
Once described by the military as a small-time extortion gang, the group attacked a remote army outpost in Butig in February, triggering a week of fighting that the military said left six soldiers and 12 militants dead.
The group also beheaded two employees of a local sawmill in April, the military has said.
The southern Philippines has been plagued by a Muslim separatist insurgency for more than 40 years, leaving more than 100,000 people dead according to government estimates.