DXMS, a Catholic church-run radio station, reported that at least three soldiers and an undetermined number of MILF fighters were killed.
The military has not confirmed those deaths.
The clashes have displaced up to 100,000 villagers in North Cotabato.
Residents of the predominantly Christian province have struggled to recover after Typhoon Fengshen ravaged farmlands in June.
"We haven't fully recovered from a natural disaster and now we're again being battered by a man-made calamity," Jesus Sacdalan, the provincial governor, was quoted by the Associated Press as saying.
Sacdalan said that the MILF fighters had looted newly harvested rice, stolen cattle, destroyed farms and set fire to 82 houses in the villages they occupied in recent weeks.
The government had given the estimated 800 to 1,000 fighters until August 9 to vacate several villages they had occupied in violation of a 2003 ceasefire.
The fighters were ordered by their leaders to pull back from the occupied villages after discussions between MILF and Philippine officials on Saturday, but the fighters later complained that their withdrawal was hampered by government troops and armed villagers.
Eid Kabalu, a MILF spokesman, said some pro-military groups shot and wounded one MILF fighter on Saturday, prompting others to delay their withdrawal for fear they could also come under attack.
Kabalu said MILF commanders were willing to withdraw if there was a government assurance they would not be attacked.
Military officials denied Kabalu's claim, saying the fighters had refused to leave the villages.
In a statement the Philippine's military said fighters in the villages "degenerated into a plain bandit group".
"All peaceful avenues have been exhausted to resolve the conflict," Brigadier General Jorge Segovia, from the Philippines military, said in the statement.
"We are now compelled to resort to the application of proportionate and justifiable force so that peace and order may be restored in North Cotabato."
Segovia stressed that the government assaults were not directed against the whole of the MILF, which has a truce with government troops.