One of the quakes - a 7.3-magnitude tremor - sent small tsunamis into Japan's south-eastern coast, but there were no reports of damage there and no tsunami in Indonesia's impoverished Papua area, Asssociated Press has reported.
Quakes were felt as far away as Darwin, said Geoscience Australia seismologist Dave Jepsen, but caused no damage in Australia.
The first 7.6-magnitude quake struck at 4.43am (0643 AEDT) on Sunday on land about 135km from Manokwari, Papua, at a depth of 35km, the US Geological Survey said. It was followed by 10 aftershocks.
At least four people died in Papua, and the airport runway nearest the epicentre was cracked, President Susilo Bambang Yudhoyono said.
Commercial flights to the area were cancelled.
Attempts were under way to search for possible victims.
The Indonesian Meteorology and Seismology Agency issued a tsunami alert, but it was revoked within an hour.
"We have not been able to get any information of casualties or damage, but since the epicentres were on land, they have a potential to cause significant damage," said Rahmat Priyono, a supervisor at the National Earthquake Centre.
Distressed residents ran out of their homes as the quake rattled Manokwari.
Thousands of residents including children and the elderly could be seen thronging the roads of the town in the darkness of a blackout and heading away from the sea despite the tsunami warning being lifted.
"The quake was quite strong and we felt it for about three minutes. The electricity blacked out after the quake," a policeman who identified himself as Ketut said.
"The police and military are working right now to help people get to higher ground due to the tsunami alert and the fact that we're on the coast," he said.
Papua, about 3000 kilometres east of the capital Jakarta, is some of the nation's least developed territory.
A low-level insurgency has simmered in the resource-rich region for years and it is largely off limits to foreign reporters.
Indonesia straddles a chain of fault lines and volcanoes known as the Pacific "Ring of Fire" and is prone to seismic activity.
A huge quake off western Indonesia caused the 2004 Indian Ocean tsunami that killed about 230,000 people, more than half of them in Sumatra.
With AFP