Papua New Guinea's Immigration and Citizenship Authority said they would be provided with residential accommodation, health services, vocational training and employment support.
But on Wednesday, the Refugee Action Coalition claimed "the offer was a sham".
"Enquiries by refugees revealed that there were no details of actual accommodation, services or allowance that would be provided in Port Moresby," the group said in a statement.
Source: Refugee Action Coalition
"Previous transfers from Manus to Port Moresby have left refugees jobless, homeless and destitute with even less access to medical care than they have on Manus Island.
"Ironically, refugees were asked to contact JDA, a service provider already under investigation for rorting its multi-million contract with the Australian government, including allegations that contracted services were not provided to refugees."
And it said 53 asylum seekers "remain incommunicado in the Australian-built Bomana detention centre" in Port Moresby.
Refugee Action Coalition spokesperson Ian Rintoul said: "relocation to Port Moresby will potentially create even worse circumstances for refugees in PNG".
"Relocation from Manus to Port Moresby even risks adding to the danger and insecurity that the refugees have already suffered," he said.
"The refugees need permanent, safe resettlement, but after six years, the government still has no options to provide protection for all those they have kept imprisoned on Manus Island."
Papua New Guinea Minister for Immigration and Border Security Petrus Thomas told the Papua New Guinea Post Courier last week the transfer is a "positive move for these men".
"Living in Port Moresby will enable them an opportunity to make their own personal decisions and move on with their lives."
In an earlier statement to SBS News, the Department of Home Affairs said: "the PNG Government is acting under its own domestic legislation and within its sovereign right."
"The Australian Government is aware that the Papua New Guinea Immigration and Citizenship Authority has offered the regional processing cohort on Manus Island the opportunity to transfer to Port Moresby," the statement said.
"The Australian Government supports PNG's efforts to resolve the regional processing caseload through this genuine offer."