Military spokesman Lt. Col. Ramon Zagala said naval personnel fought with rebels riding a variety of marine craft off the village of Rio Hondo, a crowded Muslim community in the port city, The Philippine Star reported.
Zamboanga City Mayor Isabelle Climaco-Salazar said a navy person, a policeman and four civilians were killed. She said 200 people reportedly were being held hostage in several villages.
The mayor said the violence so far was confined to the barangays, or villages, of Santa Catalina, Santa Barbara, Talon-talon, Mampang and Kasanyangan.
"We are in close coordination with our police and military authorities and everything is being done to solve the crisis the soonest possible time with minimal damage to lives and properties," she said.
About 600 residents were evacuated from Arena Blanco and Rio Hondo villages while 847 people fled to area schools and churches, the Star said.
Climaco-Salazar canceled all classes and downtown businesses have been closed.
The Civil Aviation Authority of the Philippines declared the city a "no fly zone" because of the conflict.
The Moro National Liberation Front signed a 1996 peace agreement with the Philippine government but many of its fighters kept their weapons and have accused officials of breaking a promise to develop an autonomous region for minority Muslims.
Notable deaths of 2014 [PHOTOS]