Mr O’Neill resigned on Thursday and Mr Marape was elected by parliament as the country’s 8th prime minister.
Australia is the former colonial ruler of PNG and since independence in 1975 has been its largest aid donor.
But Mr Marape flagged shift to new partners in a press conference on Friday.
“I will shift away from traditional partners and reliance on traditional partners,” he told a press conference.
“Foreign relations isn’t about politics any more, it’s about trade and commerce, and so I intend to look at Indonesia in a bigger way, I intend to look at Phillipines in a bigger way, look at Malaysia and Singapore in a bigger way.
“We’ll engage with the Chinese government as long as it is free and fair to us on our terms, we are happy just like any other engagements.
“I intend to maximise foreign relations in the economies around us."
Australia increased its foreign aid to more than $600 million in the 2019 Federal Budget, in the face of rising Chinese influence in the region.
Mr Morrison phoned his counterpart to congratulate the new leader and Mr Marape said they had a “healthy conversation”.
“No relationship is stronger and more important than the PNG-Australia relationship,” Mr Marape said.
“He did invite me to come to pay him a visit, and I did invite him to come and pay a visit, so we’ll have to do that when I find time, or when he finds time.”
In his maiden speech to parliament as prime minister, Mr Marape warned his government would be reviewing “outdated” mining and resource laws and would not be pushed around by foreign corporations.
Those comments sparked concerns by foreign investors, of which Australian companies are amongst the largest - and the PM switched to more reassuring terms during Friday's press conference.
“We are not here to chase our investors, our investors are very much part of our country and economy, and we want to maintain their presence here,” he said.
“But their presence must subscribe to the compliance of all rules and regulations. law and government policy, and maximise local content.”
A new cabinet is due to be sworn in next week but Mr Marape said his predecessor had declined a ministerial post.
Further details of his government’s policies will be revealed next Wednesday when he delivers a “State of the Nation” address.