According to the broadcaster, O'Neill said that recent movements in parliament showed "the need for change".
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The prime minister's resignation has yet to be approved by the country's Governor-General Bob Dadae.
The duties of the prime minister will be performed by 79-year-old Julius Chan, who has already served as the Prime Minister of Papua New Guinea twice, from 1980 to 1982 and from 1994 to 1997.