The Australian group the Refugee Action Coalition says five asylum seekers held in Canberra's detention centre on Nauru attempted suicide over five days last week.
It says those trying to kill themselves are Iranian or Iraqi asylum seekers transferred from Australia two weeks ago.
The Coalition says many are tricked into the transfers, initially believing they are being moved into the community like others who arrived with them.
Meanwhile, the UNHCR has visited Canberra's camp in Papua New Guinea and says the policy of detaining all asylum-seekers on a mandatory and indefinite basis amounts to arbitrary detention which is inconsistent with the obligations of both Australia and PNG under international human rights law.
The UNHCR says it is deeply concerned about the lack of a national legal framework under which refugee claims can be assessed in PNG.
Both Australia and PNG have said the camps are being operated within the law.