However, there were no immediate reports of casualties or damage.
The aftershocks hit Nabire in Papua province in the early afternoon, said Fauzi, a coordinator with the National Earthquake Centre in Jakarta.
He said his office was still processing data, but had no immediate reports of damage or casualties.
The head of Papua's meteorology and geophysics bureau, Slamet, told Elshinta radio the first aftershock was registered at 5.3 on the Richter scale.
The national health ministry put the death toll from Friday's initial earthquake and from a powerful aftershock the following day at 34, with 571 injured.
A provincial rescue agency said 30 people died while police reported 28 fatalities.
Friday's quake measured 6.9 on the Richter scale, the largest in the region since 2000.
More than 30 aftershocks have been recorded since then, including one measuring 6.2 on Saturday.
Lack of facilities
Many residents have moved into tents for fear of aftershocks and the ministry said they lacked clean water and proper sanitation.
It said apart from the injured, about 477 people were being treated for respiratory problems, malaria and diarrhoea.
Sixteen doctors will soon be sent to Nabire, the ministry said.
A police spokesman said a large quantity of food and medical aid had already arrived in Nabire in Papua's northwest, but it was still not enough.
District chief Anselmus Petrus Youw has estimated damage at $42.9 million.
Much of the town's infrastructure was damaged, including the hospital, prison, airport, local parliament, 14 schools, five mosques, nine churches and 250 homes.