New Zealand has a long-standing offer to take 150 refugees, an offer that has so far been rebuffed by Australia, which fears they may use New Zealand as a back-door entry to Australia.
Australian Prime Minister Scott Morrison said earlier this week he would allow people on Nauru to come to New Zealand if legislation was passed closing the back-door entry.
He made the comments after three Federal Liberal MPs pleaded with him to take children and their families off Nauru so they could receive proper medical care, the ABC reported.
Morrison said legislation that would prevent anyone transferred to New Zealand could not travel to Australia would need to occur first.
"There is a bill still sitting in the Senate from 2016 that would close the back door from New Zealand to Australia, which is opposed by the Labor party and the Greens and the crossbench senators preventing that protection being put in place," he said.
"I would urge them to reconsider their position on that."
Peters acknowledged that many refugees in Nauru, where the treatment has been described as inhumane, might not want to return to Australia.
"I appreciate that, but in the end it's about the standards of this country not being compromised ... We don't believe in second-class citizenship."
He said he would discuss the matter with Cabinet colleagues.
A spokesman for Prime Minister Jacinda Ardern said this week the New Zealand Government would wait to see the outcome of the Senate vote, but the offer remained the same.
The ABC said it understood the Australian Government planned to call for a vote this week on the legislation.
Close to 6000 doctors have written to Morrison demanding the government remove the 80 children from Nauru because of serious mental and physical health concerns.
"The medical situation is urgent for this vulnerable group of children," it reads.
"Medical experts, including doctors who have worked on Nauru, have spoken repeatedly about their concerns. They report widespread, significant deter orations in physical and mental health.
"We call on you to show your commitment to the strong health care system we have in Australia, which we are the guardians of, by accepting the recommendations of many medical experts and bringing these children and families to Australia so their health care needs can be met adequately, and with appropriate clinical oversight."
Ardern raised the issue with Nauru President Baron Waqa when she was on Nauru for the Pacific Islands Forum last month.
