Papua New Guinea's Prime Minister Peter O'Neill says Canberra has agreed to close the Manus Island detention centre after he met with Australia's Immigration Minister today.
The two met in Port Moresby, following which Mr O'Neill said options for closing the centre were being considered and that further announcements would be made "in due course".
There are more than 900 men held on Manus, most of whom arrived in 2013.
They come from countries such as Iraq, Iran, Afghanistan and Pakistan, and were forcibly transferred to Manus by Australia whose government has said the men will never be resettled in Australia.
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No timeline has been given for the closure but, in a statement, Mr O'Neill said "it is important that this process is not rushed but carried out in a careful manner".
"This must take into account the interests of the people of Papua New Guinea and the well-being of asylum seekers and refugees."
PNG's Supreme Court ruled in April that holding people against their will on Manus was illegal, leaving it incumbent on PNG and Australia's government to close the centre as soon as possible.
But while the PNG Prime Minister immediately said the Manus centre would be closed, Australia's government had distanced itself from responsibility over the centre.
Elements of Australia's ruling Liberal Party had suggested the Manus centre stay open, but with fewer restrictions on the movement of the detainees.
However, following signs of frustration by PNG Chief Justice Sir Salamo Injia that the governments were not complying with April's ruling, pressure has grown on Canberra to close the centre amid ongoing reports of human rights abuses.
The Manus centre has been a central pillar of Australia's policy of offshore processing of asylum seekers who come to Australia by boat.
After meeting Mr Dutton, Mr O'Neill issued a statement saying the two governments were now in agreement that the centre was to be closed.
The Refugee Action Coalition welcomed the news but said it was concerned both governments were attempting to pre-empt a full-bench Supreme Court hearing scheduled for next week.
In a statement, a spokesperson for the coalition, Ian Rintoul, said the Manus prisoners had been brutalised and tortured for over three years and deserved to be released,
"At Monday's hearing, lawyers for the Manus asylum seekers and refugees will be seeking orders for the unconditional release of all detainee and the return of all of them to Australia," he said.
"Anything less than the unconditional release and return to Australia will be a denial of justice."