The West Papua Liberation Army says four of its members have been shot dead by Indonesia's military in Tembagapura district.
The district, home to the large Freeport gold mine, is the latest focal point for conflict between pro-independence Papuan guerilla fighters and Indonesian security forces.
Police told Indonesian media the Papuan fighters killed three of their officers over the weekend and stole weapons from a local police station.
Subsequently, a Liberation Army spokesman said four of its fighters were killed, and two other people injured, in an attack by Indonesian soldiers on Sunday.
In the same area the Liberation Army launched attacks against Indonesian forces earlier this month, killing at least one Indonesian soldier and a policeman.
The Liberation army has declared war on the Indonesian state and said it will continue to target the Freeport mine.
Police told local media that with the military, their officers have tightened security around the mine.
Meanwhile, the Liberation Army spokesman rejected claims by police that the army set fire to a church in Opitawak Village, Tembagapura District.
According to police in Papua's Mimika regency, which includes Tembagapura district, the Liberation Army, which it refers to as an armed criminal group, burned the church last week.
Police say the Papuan fighters had also set fire to, and shot at residents of, local villages.
Many local villagers have evacuated the area, some with assistance of police, to avoid being caught up in the fighting, local media has reported.
Police say some of their stolen weapons have now been retrieved.