The two prime ministers met yesterday to discuss the regional resettlement arrangement of asylum seekers at the Lombrum Regional Processing Centre in Manus.
Abbott, who was accompanied by Immigration Minister Scott Morrison, stopped for the briefing en route to Indonesia.
After the briefing, O'Neill expressed support of the work done by officials from both countries in addressing the resettlement of the asylum seekers in Manus.
"We are pleased to have worked with your government on this important initiative," O'Neill told Abbott.
"The RRA (regional resettlement arrangement), combined with Australia's other maritime patrol measures, have stopped maritime people smuggling in our region and the associated loss of life at sea."
O'Neill said after an "unfortunate incident" at the processing centre in Manus, measures have been taken to improve security and management of processing at the centre.
Iranian asylum seeker Reza Barati died from severe head injuries sustained during a riot inside the Australia-run regional processing centre on Manus Island on February 17.
"There is now improved coordination between the PNG Immigration and Citizenship Services Authority, police and centre security, installation of CCTV cameras and the refugee status determination process is progressing," O'Neill said.
O'Neill said there was a lack of understanding and support for refugee settlement in PNG communities and confirmed he had instructed that a new policy be prepared with increased focus on consultations and building public awareness and support.
"The new policy will be considered by cabinet after these comprehensive public awareness and consultations are completed," he added.
O'Neill assured Abbott that PNG was committed to the implementation of the RRA but said that given its sensitivities PNG required time to work through this issues.
Following the meeting O'Neill travelled to Indonesia for the inauguration of newly elected Indonesian President Joko Widodo.
He is accompanied by Foreign Affairs Minister Rimbink Pato and State Enterprises Minister Ben Micah.
Abbott is in Jakarta to attend the inauguration.