Papua New Guinea's leader has told Scott Morrison he wants a timetable to end asylum seeker processing and get all those involved off Manus Island.
But the Australian prime minister continues to reject an offer from New Zealand to help resettle refugees, despite PNG being open to the plan.
PNG prime minister James Marape used a joint press conference alongside Mr Morrison to call for a "mutually workable" timetable on wrapping up Australia's offshore processing regime.
"We need to establish a schedule and timetable towards full closure of the entire asylum process," Mr Marape told reporters in Canberra on Monday.
"Both governments will both work in bringing this to a conclusion which is mutually beneficial."
Mr Morrison said enormous progress had been made during the talks on Monday.
"We're just going to continue to work through the issue pragmatically as we have," he said.
Mr Marape said the refugees should be resettled and those asylum seekers who had not been found to be refugees should leave PNG and return to their home countries or elsewhere.
Mr Morrison agreed, saying those who were not refugees "shouldn't be in Papua New Guinea, Australia, or anywhere else".
However, the PNG prime minister shied away from the suggestion his country could take up, independently of Australia, New Zealand's offer to resettle 150 refugees a year.
The Morrison government has refused to take up that offer for fear it would be marketed by people smugglers as a backdoor entry.
Labor says while it backs offshore processing, that comes with regional resettlement too and shouldn't turn into indefinite detention.
"Prime Minister Marape is calling for the same thing Labor has been calling on for five years - to resettle eligible refugees in third countries as a matter of priority," opposition home affairs spokeswoman Kristina Keneally told AAP.
"It's time for Prime Minister Scott Morrison and Home Affairs Minister Dutton to take action."
Greens immigration spokesman Nick McKim said he understood PNG's desire to maintain a good relationship with Australia.
"I would urge prime minister Marape to play a constructive role and do everything he can to ensure that Australia accepts the New Zealand offer because that is the quickest and simplest way to get refugees off Manus Island, which is what he says he wants to happen," he told AAP.
Manus Island governor Charlie Benjamin said if Australia would agree to the New Zealand offer, there would be no problem.
"My view is for them to go to a country as soon as possible ... but it's really Australia (that) has to step up and take those hard yards," he told reporters in Canberra.
But he didn't see moving people from Manus Island to Nauru, where Australia also has immigration facilities, as a solution, saying that would essentially be the same as staying put.
Australian Associated Press