Marine Brigadier-General Benjamin Dolorfino said the "misencounter" was halted after "there was communication" between the army and the MNLF.
"When they learnt that it's the military and MNLF fighting, they immediately disengaged," he said, but not before 13 soldiers were injured.
Almujahid Biao, the MNLF's co-chairman of a joint peace monitoring team, said no MNLF casualties were reported.
Reports from the area said six Abu Sayyaf fighters were killed, army spokesman Major Ernesto Torres Jr said, but no bodies were recovered.
The MNLF has denied striking any alliance with the Abu Sayyaf.
During the incident on Sunday, the MNLF had evacuated their camp and gathered by the roadside for easy identification.
The al-Qaeda-linked Abu Sayyaf fighters were able to escape.
Dolorfino said Abu Sayyaf fighters have often used the tactic of seeking sanctuary with the MNLF, hoping to provoke a clash between the government and the MNLF.
They try to evade gunfire by going towards other parties, he said, so that the military is forced to either stop firing or risk hitting neutral targets.
Dolorfino said the government and the MNLF were aware of the Abu Sayyaf's tactics to break the peace pact but was confident they would not succeed.
The MNLF used to be the largest Muslim group fighting for a separate Islamic homeland in the southern Philippines until it settled for limited autonomy and signed a peace agreement with Manila in 1996.
However, relations between the MNLF and the government remain rocky.
A large Jolo-based MNLF faction continues to hold weapons and has periodically clashed with government troops.
The faction, led by jailed Muslim rebel leader Nur Misuari, has been suspected in the past of supporting the Abu Sayyaf.
And this month, Dolorfino and 19 companions were virtually held hostage for two days by MNLF guerrillas demanding more benefits under the 1996 peace accord.
The government, which has been engaged in a months-long offensive against the Abu Sayyaf, believes the group has been severely weakened by the loss of two top leaders who were killed on Jolo last September and in January this year.