The court is considering who has legal responsibility for hundreds of detained men after it ruled Australia's processing centre on the island was unconstitutional and should close.
Lawyer Ben Lomai says there has been no action by Australia or Papua New Guinea since the Supreme Court declared the processing centre on Manus Island unconstitutional in April.
The PNG government had said it would close the facility and ask Australia to find alternative arrangements for the hundreds of asylum seekers and refugees held there.
Mr Lomai, who represents some of them, says lawyers have been forced back to court later this month, on August 22, to argue for the order to be enforced.
He says the PNG government has already been asked to present a resettlement plan but was wrong to tell the court it would assume full legal responsibility.
"We take a different view on that, especially on the basis that we say that, after the April 26 Supreme Court decision, that decision has changed, which means that it nullifies the entire arrangement between Papua New Guinea and Australia and, therefore, has discharged the onus, or obligation, on the PNG government to be responsible for the asylum seekers. We are saying that the Australian government is solely responsible."
Ben Lomai says, at the least, the Supreme Court is expected to say both countries are equally responsible.
He says Australia needs to do the right thing for the people it has been sending to Manus Island under a regional resettlement program signed with Papua New Guinea.
"We can't enforce the order of the Papua New Guinea Supreme Court against the Australian government, but we are of the view that, morally, the Australian government should accept that position in law as would be interpreted by the Papua New Guinea Supreme Court and they should be able to abide by that, especially where they have relations with the PNG government and to which such an offshore program has been established on Manus Island. So, in a way, they should take some more responsibility. Morally, they are obligated, in our view."
The Melbourne-based Human Rights Law Centre says relocating the men to Nauru, the site of another Australian detention camp mired in controversy, would be harmful.
And it says resettling them in Papua New Guinea is unrealistic.
Executive director Hugh de Kretser says the only sustainable solution is to transfer them to Australia.
"It's a legal mess, if you like, which the most sensible thing the PNG and Australian governments can do to fix is to end up by bringing them here to safety. At the moment, they're in a, if you like, holding pattern, where they have opened the gates, they're pretending everything is fine. But they have to come back before the court to answer to the court why the detention centre is continuing and what their plans are around the 900 or so people who are held there. And that will engage other human rights under the PNG constitution, which has reasonably strong human-rights protections, unlike Australia's constitution."
The Department of Immigration says Australia is not a party to the proceedings and, because the matter is before the court, it would not be appropriate to comment.
The department says in a statement it has not been ordered to appear before the court and, contrary to media reports, Australia is not required to prepare a resettlement plan.
Ian Rintoul, from the Refugee Action Coalition advocacy and support group, has been in Papua New Guinea, attending the hearings.
"Usually, there are a number of Australian officials from the High Commission sitting there maintaining some observation, taking notes, there are other Australian lawyers, representatives of the Department of Immigration and Border Protection. They were nowhere to be seen on that particular day. There is really no question whatsoever that the Australian government is doing everything it can to distance itself from the Supreme Court finding. It tries to say that it is not a party to these proceedings. Therefore, it can treat the PNG Supreme Court and the ruling it was unlawful with complete contempt."
When the Labor Government and Papua New Guinea struck their deal before the 2013 federal election, the Manus Island facility was part of a broader resettlement plan.
Australia would transfer asylum seekers arriving by boat to remote overseas camps, and anyone granted refugee status could only ever be settled there or in another regional country.
Mounting allegations of abuse, mistreatment, neglect and secrecy from within the offshore system have led to heavy criticism of the Manus Island and Nauru operations.
That criticism has come from human-rights groups, medical and legal experts, even the United Nations.
The Human Rights Law Centre's Hugh de Kretser says he believes the Australian government understands how significant the PNG developments are.
"There's no doubt that they would be scrambling to respond to what the PNG Supreme Court has ordered, but, publicly, they're pretending like it's business as usual, when it can be anything but."
