The epicentre was recorded 125 kilometres east of the town of Kimbe according to the United States Geological Survey, which said it struck at a depth of around 40 kilometres.
A Pacific-wide tsunami is not expected and there is no tsunami threat to Hawaii, the Pacific Tsunami Warning Center said in a bulletin.
The island of Bali was also struck by a magnitude 6 quake on Thursday, the US Geological Survey said.
The Pacific Tsunami Warning Centre said that hazardous waves were possible on coasts within 300 km (186 miles) of the epicenter.
Speaking by phone from Rabaul police station, Constable Roy Michael said he felt the quake but "it was not too strong".
He said there was no damage in the town, but officers had not yet been able to contact villages closer to the epicentre.
Australia's Tsunami Warning Centre said its coastlines were not at risk.
Scientists don't have tide gauges close to the where the natural disaster happened and weren't able to say whether any tsunamis were generated.
He says areas farther away are unlikely to be affected because of the natural disaster isn't "terribly large" and many are shielded by land masses and islands.
The initial magnitude 7.0 quake that triggered the tsunami threat along Papua New Guinea's coasts.
At least two aftershocks with a magnitude greater than 5 shortly followed.
No reports of damage or injuries have surfaced from the quake.
Papua New Guinea, like Indonesia, is located on the Pacific "Ring of Fire", a seismically active region that encircles the Pacific Ocean.
Indonesian authorities said at least three people were killed and four injured in the quake.
Indonesia's disaster agency says the September 28 disaster that hit Sulawesi Island has killed 2045 people. But officials have warned that as many as 5,000 people may have died in the quake, which turned the ground in areas around the city of Palu into liquid via a process called liquefaction (as seen in the top video).