Thousands of people have fled their homes in the islands following this week's clashes, the worst of any religious conflict in the country's 50-year history.
A police spokesman said the latest clashes began at dawn and were continuing several hours later - there were no details about how the violence started, nor whether there were any casualties.
A military statement said there had also been several hours of fighting during the night in the provincial capital city, Ambon, where the military took control on Wednesday.
The Indonesian army has imposed an overnight curfew in parts of the region according to a general commanding troops in the area.
"We have limited people from going around at night," Brigadier General Max Tamaela said.
Thousands of people have fled their homes in the islands following this week's clashes, the worst of any religious conflict in the country's 50-year history.
Christians and Muslims have clashed in Ambon in Maluku province, and in the town of Tobelo on the island of Halmahera in North Maluku province.
Some 12,000 people from both provinces have sought refuge from the fighting in army and police barracks and other installations, according to a military statement.
Christian leaders have appealed to the United Nations to send in peacekeepers to prevent the violence from escalating.
War zone
The clashes started in Ambon last Sunday, apparently sparked by a road traffic accident in which a Christian driver hit a Muslim boy.
Rioting broke out in Trikora Square, in the centre of the port city, with people using guns, slingshots and home-made bombs.
Eyewitnesses said parts of Ambon looked like a war zone, with decapitated bodies on the streets.
The main Protestant church was burned down, as well as a mosque.
The Indonesian military sent in reinforcements to restore the peace, and on Friday the city was described as "quiet but tense".
The violence, in which over 70 people were killed, sparked three days of clashes on Halmahera Island.
Thousands of Christians, who dominate the area, went on a rampage in the town of Tobelo and surrounding villages, burning houses, businesses and Muslim places of worship.
More than 250 people were killed in what the BBC's correspondent Richard Galpin described as the worst incident in a year of violence in the region.
Health risks
The humanitarian group Medecins Sans Frontieres (Doctors Without Borders) has warned that health conditions in the Moluccan islands are deteriorating because of the fighting.
It said that medical supplies could not be delivered, people in need of care were trapped and health staff were afraid to travel.
"The risks are getting bigger that children will die of curable diseases as the parents cannot get access to health care" Richard Rowat, a group official in Ambon, told the Associated Press.
No martial law
More than 2,000 Indonesian troops are trying to restore peace on the islands. Extra troops have been sent to Halmahera, which is now reported to be quiet.
However, Indonesian President Abdurrahman Wahid has ruled out imposing martial law.
He admitted the situation was out of control, but insisted martial law would not be the right answer.
More than 1,000 people are thought to have died in the Moluccas since last January.