The first quakes were reported on the island early on Wednesday at 7.26am local time (Tuesday 9.26pm GMT), topping 6.4 on the Richter Scale.
The US Geological Survey (USGS) has since noted preliminary 6.6 magnitude tremors at a depth of 70 miles (112 km) below ground.
The quakes truck some 51 miles (83 km) west of the coastal hub of Wewak.
In its report, the USGS said: “An earthquake with a preliminary magnitude of 6.6 occurred in New Guinea, Papua New Guinea at 2127 UTC on Tuesday November 7, 2017.
“Based on all available data there is no tsunami threat from this earthquake.
“No action is required.”
The news comes three days after a powerful earthquake struck the Pacific island of Samoa.