The Refugee Action Coalition says an asylum seeker originally held in detention in Nauru has given birth in Australia.
The group says this goes against the Australian immigration minister Scott Morrison's claim last month that Canberra would make no concessions to asylum seekers, including pregnant women, sent to Nauru.
It says it is now clear that even his own department does not think there are adequate medical facilities for pregnant women on Nauru.
The group's Ian Rintoul says it was always irresponsible of Mr Morrison to insist that a twin birth would present no problems on Nauru.
He has again criticised the poor conditions in the Nauru camp, saying the rationed five-minute showers have to be taken together with the children and the shortage of water means the shower is a trickle of water.
Since July, Australia sends asylum seekers arriving by boat to Nauru and PNG for processing but determinations reached so far have been kept secret.