New Zealand is prepared to accept some asylum seekers that Australia has sent to detention camps on impoverished Pacific island nations.
However there appeared to be little chance Australia would take up the offer, made by New Zealand's prime minister John Key.
The debate is over whether New Zealand should take Australia's unwanted asylum seekers, from the Middle East and Asia.
It comes amid an uproar over what will happen to 267 asylum seekers who are expected to be transferred from Australia to the Pacific atoll of Nauru.
The issue of their fate was raised in annual talks between Australian prime minister Malcolm Turnbull and his visiting New Zealand counterpart.
Australia refuses to allow any asylum seekers who try to reach the country's shores by boat to ever settle in Australia, and sends them instead to detention camps on Nauru and Papua New Guinea.
The policy has virtually stopped asylum seekers from the Middle East and Asia attempting to reach Australia on rickety boats.
The 267 asylum seekers came from Nauru's detention camp to Australia for medical treatment or to support a relative who needed treatment.
They refused to return to Nauru pending an Australian High Court challenge to the legality of Australia's refugee policy, but the court recently ruled against them, leaving them at risk of deportation.
The court decision sparked outrage among refugee advocates, two of whom climbed to the top of a 500 foot tower in Melbourne on Friday to unfurl a banner with the Twitter hashtag LetThemStay.
Mr Key's government reached an agreement in 2013 with Australia to resettle 150 refugees a year from Nauru and Papua New Guinea.
On Friday, Mr Key said the offer still stands, provided the asylum seekers meet New Zealand's character requirements and are genuine refugees.
"So I can't tell you who might or might not be able to come, or whether the Australian government would want to exercise the right to do that," Mr Key told reporters in a joint press conference with Mr Turnbull.
"All I can simply say is the offer remains on the table."
But Mr Turnbull appeared to dismiss the offer, saying the government did not want to give people smugglers "marketing opportunities" to recruit asylum seekers from countries such as Bangladesh, Iran and Afghanistan to embark on the dangerous journey.
"We take into account what John has proposed ... but we do so very thoughtfully, recognising that the one thing we must not do is give an inch to the people smugglers," he said.