Australia's Human Rights Law Centre says the Australian Government must ensure the safety of people it is detaining in Papua New Guinea.
It said it was making the call as PNG's Pandemic Response Controller warned a coronavirus outbreak could overwhelm the health system within days.
There are currently more than 175 people in PNG and 185 in Nauru detained under Australia's offshore detention scheme.
PNG's Covid-19 cases have risen exponentially over the past two weeks and most cases were in Port Moresby, where refugees who were detained on Manus Island remained in limbo.
PNG 's Response Controller, David Manning, said Covid-19 was now 'widespread' throughout the capital and an isolation facility there was working at capacity.
The Prime Minister James Marape had earlier warned the PNG health system would struggle to deal with a widespread outbreak.
One of the detained refugees, Shaminda Kanapathi, is a human rights activist who says "after years spent in detention we are all susceptible to Covid-19."
Kanapathi said the refugee's health had been left to deteriorate over recent years without proper access to medical facilities for physical or mental health.
"Many of us already have compromised auto-immune systems and PNG does not have the capacity to look after non-residents."
The Human Rights Law Centre's David Burke said the Australian government has always been responsible for the people it has detained offshore.
"That duty of care does not disappear during a pandemic. Everyone deserves to be safe in this public health crisis including the people detained in PNG and Nauru."