The prime ministers met at the Asia-Pacific Economic Cooperation forum in Bali this week, with regional border security and the transfer of asylum seekers to Manus Island a main focus.
Policing, law-and-order and the provision of 50 Australian Federal Police officers for secondment to PNG were also discussed.
"We are in complete agreement that people smuggling must be defeated, and that regional border security was a challenge for both our nations and our regional partners," O'Neill said in a statement.
"I am delighted to be able to inform the people of Papua New Guinea that the Australian Prime Minister endorsed the Manus Agreement that is seeing the significant development of the Manus detention centre.
"I confirmed to Abbott that Papua New Guinea would play its role in strengthening border security in our region, and that we will work hand in hand with his Government in particular in doing so."
"People smuggling is not just a problem for Australia and Indonesia. It is a problem for PNG and other regional nations."
O'Neill welcomed the new Australian government's focus on cutting bureaucratic processes in delivering development assistance or aid.
"We are committed to working with the Australian government in ensuring the aid program is more visible, and delivers outcomes that help strengthen our government-to-government and people-to-people relationship," he added.
The prime minister also confirmed he had invited Abbott to visit PNG.
"My government and I look forward to working with Abbott, Foreign Minister Julie Bishop and their colleagues in adding new dimensions to our most important bilateral relationship in the future," he said.