The quake hit the provinces of Southern Highlands and Hela, a remote and heavily forested area 560km north-west of Port Moresby, early Monday, cutting off communication and transport connections.
At least 13 people were believed to have been killed in Mendi, the capital of Southern Highlands, and 18 others died in the Kutubu and Bosave areas, PNG's Post Courier newspaper reported, citing Hela provincial administrator William Bando.
More than 300 people were reportedly injured.
PNG's department of geohazard management said more aftershocks were likely, with the largest so far measured at magnitude 5.5.
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