Negotiations between the government and the MILF, which wants an expanded Muslim region in the south, fell apart last month.
MILF has been waging 30-year guerrilla war for separate Islamic state in south of largely Christian Philippines
Conflict has killed more than 120,000 people
Separatists signed ceasefire with government in 2003 to open way for peace talks
Both sides initialled draft agreement for recognition of MILF's 'ancestral domain' in south in July
But agreement on size of Muslim homeland and future government's powers halted amid protests by Mindanao Catholic politicians
Supreme court suspended draft accord, raising new tensions and re-igniting fighting that had been mostly dormant since 2003
MILF fighters led by at least one of the commanders now hunted by the military, went on a rampage, burning homes and killing residents in two towns after the supreme court halted a scheduled signing of a peace deal with the government following opposition from Roman Catholic politicians.
Gloria Arroyo, the Philippine president, dissolved a government peace panel negotiating with the MILF last week, saying the government would no longer negotiate with the separatists.
Scores of civilians have been killed and more than half a million people have lost their homes and livelihoods since the peace process broke down.
With mounting civilian casualties and a growing refugee crisis, the military operations may be turning the people in the south against the government.
MILF leaders have said the three commanders are out of their control, but the government says peace talks cannot resume until they are in custody.
Al Jazeera's Veronica Pedrosa, reporting from an MILF camp in Mindanao, said the prospects for peace talks resuming appeared to be very dim.
The group's leaders said the renewed fighting was a direct result of the government's failure to stand by its commitments in the proposed peace pact that was initialled in July.
And the fighters seemed very motivated, well armed, disciplined and were preparing for further conflict, so the worst may be yet to come, our correspondent said.
The International Committee of the Red Cross, which is already identifying new evacuation centres in case of a larger exodus of civilians from the conflict zone, has appealed to fighters and troops not to harm civilians as they battle each other in the worst fighting in the southern Philippines since 2003.