Australia's human rights watchdogs want the health needs of every asylum-seeker child on Nauru immediately assessed.
National Children's Commissioner Megan Mitchell says there is likely a systemic issue causing health problems for children on the Pacific island.
"I urge the government to undertake comprehensive assessments of all children on Nauru and expedite their transfer to Australia for treatment where health needs are present," she said on Tuesday.
"These children's health care needs should be addressed as a matter of urgency."
Human Rights Commissioner Edward Santow said a number of medical and human rights bodies had expressed concern about the health of asylum seekers on the island.
"Australian and local authorities should proactively ensure that everyone who requires medical care in Australia is transferred immediately," he said.
Prime Minister Scott Morrison talked down the prospect of a deal with Labor over resettling Nauru- based asylum seekers in New Zealand.
Labor wants a proposed lifetime ban to only apply to New Zealand-resettled asylum seekers coming off Nauru.
Mr Morrison told reporters in Canberra on Tuesday that resettling people in New Zealand had never been his preferred outcome.
He said it could undermine the deal struck with the United States and unwind tough border policies.
"You don't get children off Nauru by putting more children on Nauru through weaker border protection policies," Mr Morrison said.
He said he was concerned, as were doctors, about the mental health of children on Nauru and would bring them to Australia for treatment on a case-by-case basis.
Home Affairs Minister Peter Dutton said 13 children on Nauru were in family groups in which adults were "subject to adverse security assessments from the United States".
Opposition immigration spokesman Shayne Neumann earlier said Labor was willing to work on amendments to the laws.
"You can be strong on border protection, resettlement, but the truth of the matter is these people have stayed there too long," he said.
Australian Border Force confirmed 11 children in detention on Nauru have been transferred to Australia to receive medical treatment.
Fifty-two children remain on the island.
About 652 people, including 107 families, were on Nauru, while 626 men were on Manus Island in Papua New Guinea, Border Force told Senate estimates.
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