Signs posted around the centre on Tuesday evening informed refugees they could "apply" to go to Nauru by completing an "expression of interest" form by October 23.

The move - which would transform the refugee population on Nauru, which was previously set aside for families - was strongly condemned by refugee advocates, human rights organisations and the Greens, who said it was simply shunting people from one island "prison" to another.

The transfer was only available for refugees who had applied for resettlement in the United States, the signs said. Their applications to the US would remain unchanged, but they would also have the option of staying in Nauru for up to 20 years.

"The government of Nauru will then decide which refugees can transfer," the refugees were told. "Transfers will not affect [the] eligibility or progress of US resettlement applications."

A spokeswoman for the Department of Immigration and Border Protection confirmed the Nauru offer and said it would remain voluntary. "No one will be forced to move to Nauru," she said.

The Australian and Papua New Guinean governments have agreed to close the regional processing centre on Manus Island by October 31, following a PNG court ruling last year.

As the centre has been progressively dismantled, refugees have been offered alternative accommodation in the nearby township of Lorengau.

???But most have refused to move, citing concerns for their safety amid rising tensions between refugees and local Manusians.

Behrouz Boochani, an Iranian refugee and journalist at the centre, said demolition continued on Tuesday but refugees did not want to go to either Lorengau or Nauru.

"It's completely unacceptable that after more than four years the Australian government still refuses to solve the problem by taking the refugees to a safe place," he said.

Daniel Webb, director of legal advocacy at the Human Rights Law Centre, said the Nauru offer showed the government was "scrambling" to meet the October 31 closure deadline.

"They keep saying they'll close the Manus facility in three weeks but they know there is nowhere safe for the men trapped inside it to go," he told Fairfax Media.

"After four long years filled with fear, limbo and violence, it's not good enough to just transfer suffering from one island to another."

Amnesty International senior research director Anna Niestat said Immigration Minister Peter Dutton was "desperately trying to find ways to mask rather than solve the problem".

And Greens immigration spokesman Nick McKim said the move "absolutely reeks of panic and desperation".

However, the possibility of transferring refugees from Manus to Nauru has been open since at least May, when Immigration Department secretary Mike Pezzullo confirmed three-way talks were under way.

He told a Senate estimates hearing the government had "noted" an offer from Nauru to accept men from Manus, and said: "We are in discussions with the government of Nauru about the possibilities that that creates."

Nothing had been concluded at that stage, Mr Pezzullo said. Nauru has historically received a monthly payment from Australia of $3000 per refugee as part of the regional processing arrangement.

According to an official Operation Sovereign Borders update on Tuesday, 742 men remained at the regional processing centre on Manus Island at the end of September, and 369 people on Nauru.

However, there are close to 900 other refugees living in the community in Nauru, and dozens of men in PNG living at the East Lorengau Refugee Transit Centre or at a hotel in Port Moresby.

The US has so far accepted 54 refugees for resettlement, who left the islands late last month. The country is expected to take up to about 1250 people under an agreement struck between Malcolm Turnbull and Barack Obama, which Donald Trump agreed to honour.