The man, Omid, was flown to Australia on Thursday, 24 hours hours after he set himself alight in apparent protest in front of visiting United Nations officials.
But he died in a Brisbane hospital Friday afternoon.
The Refugee Action Coalition's Ian Rintoul said the lack of experienced staff; the lack of medical supplies; the lack of attention; the shocking conditions at the Nauru hospital and the delay in arranging for the man to be medivacced from Nauru has cost him his life.
He said those responsible must be held to account.
Mr Rintoul said offshore detention claimed another life and that Omid's name will be added to the names of Reza Barati and Hamid Khazaie.
He also questions how many more lives and souls are to be lost before the Australian government will face up to its hypocrisy of declaring that offshore detention is about saving lives at sea, while lives are destroyed in their detention camps.
Mr Rintoul said the Australian government must bring all those on Manus Island, Papua New Guinea and Nauru to the Australian mainland.
He said just like the case of Hamid Khazaie, who needlessly died of septicaemia in 2014, there will be a coronial inquiry that can reveal the shocking conditions and political decisions that led to Omid's death.
Reza Berati was allegedly beaten to death inside the Australian-run asylum seeker processing centre on Manus Island, Papua New Guinea in February, 2014. Two men were found guilty of his murder.
Ian Rintoul said asylum seekers and refugees on Nauru have yet another reason to maintain their protests and to maintain their rage at a system that took Omid's life and just as surely systematically destroys theirs.
A vigil was held Friday night at the Nibok the settlement where Omid set fire to himself.
Today will be the 41st day of protest by the asylum seekers in the family camp on Nauru.
Last week, another Iranian refugee reportedly splashed himself with petrol and set himself alight before neighbours intervened with a fire extinguisher.
Meanwhile, the future of asylum seekers sent by Australia to Papua New Guinea's Manus Island remains uncertain, after a PNG court ruling that their detention was illegal.