Scott Morrison and Peter Dutton have talked down the prospect of a deal with Labor over asylum seeker resettlement, stepping away from a proposal flagged during the Wentworth by-election.
Labor is weighing up whether to back draft laws, introduced by the coalition two years ago but not passed, to place a lifetime ban on resettled asylum seekers being allowed to enter Australia.
One of Labor's conditions is for the lifetime ban to only apply to New Zealand-resettled asylum seekers coming off Nauru.
The Wentworth by-election reignited debate over the fate of asylum seekers on Nauru and Manus Island, some of whom have been there for five years.
During the campaign, the coalition flagged the possibility of accepting a New Zealand offer to take in 150 refugees if the "backdoor entry" ban was legislated.
Mr Morrison told reporters in Canberra on Tuesday resettling people in New Zealand had never been his preferred outcome.
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.
"What I'm going to do is continue on the program that I have been working with some crossbenchers on very carefully, not in a big-noting way ... managing the issues case by case, talking to those who understand the mental health and physical health issues," Mr Morrison said.
Home Affairs Minister Peter Dutton said there was a further problem in that 13 children on Nauru were in family groups in which adults were "subject to adverse security assessments from the United States".
Mr Dutton doubted whether New Zealand would take people who posed a security risk.
"Are they suggesting that we should separate the children from the parents, leave the parents in Nauru but bring the children here?" Mr Dutton said.
Opposition immigration spokesman Shayne Neumann earlier said Labor was willing to work with the government, and sent a letter to Immigration Minister David Coleman on Monday night outlining amendments.
Mr Neumann said the time had come for the government to meet Labor halfway.
"You can be strong on border protection, resettlement, but the truth of the matter is these people have stayed there too long," he said.
The issue was not raised in the Labor caucus meeting on Tuesday.
Meanwhile, Australian Border Force confirmed 11 children in detention on Nauru have been transferred to Australia to receive medical treatment.
The revelation came at a Senate estimates hearing on Monday, with ABF saying an unknown number of adult refugees and asylum seekers had travelled with them.
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.
