The attack happened on Tuesday in the village of Kairatu, 50km (31 miles) north-east of Ambon, the main city in the Moluccas.
A police spokesman denied accusations by a local lawyer that Christians in the area were killed because they refused to convert to Islam.
The deaths have shattered a period of relative calm in the spice islands, where thousands of people have been killed in almost two years of religious violence.
Civil emergency
"It started from an attack from the white group on the reds in the village," said National police spokesman Brigadier-General Saleh Saaf, using the local terms for the two religious enemies.
But the deaths were on both sides, he said.
"It is not true that the victims were people who did not want to convert to another religion," he said.
Semmy Waileruny, a Christian community leader and lawyer in the Moluccas, said Muslim groups had attacked several villages in recent days and were forcing Christians to convert and killing those who refused.
One policeman in Ambon, 2,300km (1,400 miles) east of the Indonesian capital, Jakarta, said there were regular reports that both sides were attempting to force conversion to Islam or Christianity.
Despite declaring a state of civil emergency, Indonesian President Abdurrahman Wahid has been unable to end the killings in the Moluccas, once a popular tourist destination.
The government said in October that it might lift the civil emergency - which is one step below martial law and allows security forces to search houses, detain suspects and impose a curfew. However it has made no move to do so.
EU concern
The population of the Moluccas is almost equally divided between Christians and Muslims.
Since the conflict began, tens of thousands of people have fled the Moluccas for other parts of Indonesia, which is mainly Muslim. Many are living in squalid refugee camps.
On Tuesday the European Union said it was "deeply concerned" by violence in several Indonesia provinces, including Aceh, the Moluccas and Irian Jaya. It called on the Indonesian Government to use diplomacy rather than force.
"The European Union has spoken out on a number of occasions in favour of a strong, united, democratic Indonesia [and] fully supports the country's territorial integrity," the French EU presidency said in a statement.