Refugee advocates in Australia say there are 27 asylum seeker children remaining on Nauru after multiple families were flown to Australia for medical treatment.
The Asylum Seeker Resource Centre says a total of 25 people - eight children as part of six families - left the Pacific island on Monday.
The asylum seekers remaining on Nauru and Manus Island have critical and serious medical issues, ASRC spokeswoman Jana Favero says.
"Everyone's had enough. The Australian government sponsored offshore detention medical crisis needs to end now," she said in a statement.
"After five years, every moment is too long."
However, once the families receive medical treatment they will not be resettled permanently in Australia.
Home Affairs Minister Peter Dutton last week confirmed all asylum seeker children would be taken from Nauru by the end of this year, but non-refugees would be made to go back to their country of origin.
Refugees would be sent to the United States or resettled in other countries.
A Labor government would also ban the asylum seekers from permanently settling in Australia, with the opposition's policy centred on offshore processing and third-country resettlement.
The New Zealand Government has offered to resettle 150 asylum seekers from Australia's offshore detention centres on Nauru and Manus Island and Prime Minister Jacinda Ardern last month said the offer still stands.
"We've always said that of course we would want to see children in particular, and women and children a particular priority," Ms Ardern said.
Australia is concerned asylum seekers sent to New Zealand could later move to Australia, their original goal.