Worsening mental health has left some of the children among the refugees in a "semi-comatose state", unable to eat, drink or talk, humanitarian group Médecins Sans Frontières (MSF), which was ejected from Nauru, said, Reuters reported on Saturday.
The United Nations refugee agency, UNHCR, said on Friday that more than 1,400 people are still being held on both islands, which have hosted Australia-bound migrants and asylum-seekers since 2013.
The refugees were transferred to the islands after being intercepted trying to reach Australia by boat, a policy widely criticized by the United Nations and other rights groups.
"This policy has failed on a number of measures," UNHCR spokeswoman Catherine Stubberfield said in a statement. "It's failed to protect refugees, it's failed to provide even for their most basic needs."
Of the 12 people who have died since Australia began detaining migrants and refugees offshore, half had been confirmed or suspected suicides, the agency said.
"Ultimately, responsibility lies with Australia for those who have sought its protection," Stubberfield said in the statement on the agency's website.
"This is a system designed, financed, managed by Australia, and it's Australia which must be accountable for the full gamut of those consequences."
Australia's Department of Home Affairs did not immediately respond to a request from Reuters to seek comment.
In a statement to the Guardian newspaper, it said it treated the health of refugees "seriously".
It added, "All transferees on Nauru are free to move around the island; they are not in detention."
A contracted provider offered services such as general practitioners, nursing and mental healthcare clinics throughout the week, in addition to after-hours staffing for emergencies, it said in the statement.
As many as 65 health professionals, including 33 mental health professionals, provide services to transferees on Nauru, it added.