Prime Minister John Key says he will ask his Australian counterpart to release New Zealanders from detention centres and exempt them from Australia's tough new immigration policy.
About 200 New Zealanders convicted of crimes have been placed in detention centres while they await deportation.
Malcolm Turnbull is visiting New Zealand later this week, and opposition parties said it was Mr Key's opportunity to demand change.
Mr Key said he believed only the most serious criminals should be deported, and people's ties to Australia should be taken into account.
He told Morning Report he was reasonably confident some change would happen.
The visit will be Mr Turnbull's first overseas trip as prime minister - he ousted Tony Abbott as the Australian Liberal Party leader nearly a month ago.
Green Party co-leader James Shaw hoped Mr Key would do more than just raise the subject.
He said Mr Key needed to be very clear to Mr Turnbull that Australia's treatment of detainees was not acceptable.
"Australia and New Zealand have a very close relationship and one of the advantages when you have a close relationship is that you should be able to talk straight with each other."
"Rather than pussy-footing around, I think we need to be straight with the Australians," Mr Shaw said.
Labour Party leader Andrew Little, who will also have an official meeting with Mr Turnbull on Saturday, said it was acceptable for Mr Key to be assertive.
He said that was what New Zealanders wanted to see from Mr Key.
"He's got to lay it out very clearly," Mr Little said.
Mr Little hoped the meeting would result in genuine change, and was not just a back-slapping exercise between the two prime ministers.
Labour's foreign affairs spokesperson, David Shearer, said he was surprised Mr Key had not done something sooner.
"They've certainly been negotiating about these people who are going to be sent back to New Zealand for the last few months. In my understanding there are a thousand people waiting to be sent back to New zealand, which will have an enormous impact."
Mr Shearer said retaliating against Australia by implementing a similar immigration policy would not improve matters.
In his own statement, Mr Turnbull said it was appropriate that his first destination was New Zealand, given the two nations' close relationship.
He said climate change would be one of a number of issues that would be discussed - as well as the movement of citizens between Australia and New Zealand.
Mr Turnbull will be travelling with his wife Lucy, and the pair will join Mr Key and his wife Bronagh for a private dinner on Friday evening before the official programme begins on Saturday.