It reported that at least 13 died in the Southern Highlands capital Mendi while 18 others were believed to have been killed in nearby Kutubu and Bosave.
Some 300 people were injured, it added, and properties destroyed, with reports of landslides and sinkholes.
The Papua New Guinea Today website, quoting Catholic priest Pius Hal, said at least 10 died, including four children, in quake-triggered landslides.
AFP was unable to confirm the death toll.
A government assessment team was due to fly into to the area Tuesday to get a better idea of the impact, with the military mobilised to help restore services and infrastructure, the government's Chief Secretary Isaac Lupari said in a statement.
"Information will be provided as this is made available from assessment teams in the area," he added.
The tremor hit at a depth of 35 kilometres around 3:45 am (1745 GMT Sunday), US seismologists said, with aftershocks of 6.0 and 6.3 magnitude recorded.
The region is home to oil and gas production. ExxonMobil PNG said buildings at its Hides Gas Conditioning Plant were damaged but all its staff were "safe and accounted for", with non-essential employees to be evacuated.
Australian resources company Oil Search on Monday said its operations in the area were being shut down as a precaution and for damage assessment, and there were no injuries reported among its staff so far.
Earthquakes are common in PNG, which sits on the so-called Pacific Ring of Fire, a hotspot for seismic activity.