"I really hope Australia does take up our offer, we are here to help," Immigration Minister Iain Lees-Galloway said on Friday.
"We would like to work with Australia to help find a compassionate solution to this."
About 600 refugees have barricaded themselves inside the now closed camp on Manus Island, off the coast of Papua New Guinea, fearful they'll be attacked by locals if they venture outside.
They have no power, no water and mosquitoes are causing concerns about malaria.
Iranian Behrouz Boochani said New Zealand was his best chance of resettlement.
"We are asking New Zealand to seriously have negotiations with the Australian government to take us from this prison," he said.
"Our message is to put pressure on the Australian government to accept the offer. We have been here for more than four years."
New Zealand Prime Minister Jacinda Ardern will discuss the Manus Island situation when she meets Australian counterpart Malcolm Turnbull in Sydney on Sunday.
Mr Lees-Galloway wouldn't comment on the way the crisis is being handled.
"It's a challenging situation for Australia, they face issues that we don't in New Zealand," he said.
Australian authorities say alternative accommodation on the island is ready for the refugees.
New Zealand's offer to take 150 refugees in Australia's offshore detention centres was first made in 2013.
It has been rejected several times on the grounds that it would offer refugees a back door into Australia and could be used as a marketing ploy by people smugglers.
