Australia, the United States and other allies are seeking to counter China's growing influence in the region after China signed a security pact with the Solomon Islands.
Defence Minister Richard Marles said Australia wanted to elevate its security co-operation with PNG as soon as possible.
Mr Marles said the region was dealing with a complex and challenging strategic environment.
"This is a time where you need to be close to friends and that's how we feel in relation to PNG," he told reporters in Port Moresby.
Mr Marles said Australia needed to be deeply engaged in the Pacific and help island nations develop.
"Defence is a really critical way in which we can do that," he said.
Mr Marles said Australia hopes to finalise the agreement as soon as possible but did not commit to a timeline.
Prime Minister of Papua New Guinea James Marape acknowledged the importance of Australian ties but said parts of the relationship could be strengthened.
"There is no greater relationship PNG has," Mr Marape said.
"We want to tidy on other areas of our relationship that should be better, to strengthen our bilateral relationship going forward."
Following the security deal struck in April, more than 30 police officers from the Solomon Islands landed in China this week for training.
The Chinese embassy in the Solomons said the exchange would "improve better understanding of Chinese police, diversified Chinese cultures and friendly Chinese people".
Australia insists it remains "security partner of choice" for the Solomon Islands but some foreign policy experts hold serious doubts.
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