Prime Minister John Key wants to make it easier for New Zealanders living in Australia to gain long term residence.
It comes after many New Zealanders affected by the Queensland floods weren't able to access Australian government grants.
Key says that about 100,000 kiwis are left effectively stateless because they don't receive support from either government.
Key is in Australia for talks with Australian Prime Minister Julia Gillard.
He is accompanied by seven of his ministers, for meetings with their Australian counterparts and a joint cabinet meeting tomorrow.
Issues around economic alignment will be addressed, including emission trading schemes and a joint agency to oversee information and recalls for medicine.
There will also be discussions over the 100 year ANZAC anniversary which falls in 2015.
Key and Gillard held a joint press conference tonight on the 2015 Cricket World Cup, which Australia and New Zealand will co-host.
While it was light on any new detail, Key was full of assurances New Zealand can do a good job.
Key is attending the Australian Tennis Open tonight as a guest of Gillard, to watch the women's singles final.
PM looks to free up travel across the ditch
Key is also pushing fresh moves to speed up trans-Tasman travel - including passport-free travel for holidaymakers.
But he may meet resistance, with Australia looking to tighten border checks, rather than loosen them.
Australia wants data sharing to allow criminal checks at trans-Tasman borders, a move which will be discussed during talks this weekend in Melbourne.
The Australian move follows a spate of high-profile cases - including New Zealander Hohepa Morehu-Barlow being charged with stealing nearly $20 million from Queensland Health.
In a piece headlined "Crook as, Bro", an Australian newspaper reported at the weekend that Kiwi convicts were lying their way into Australia, including one man who spent four months working at the Australian prime minister's residence, despite a criminal record.
He lied on his passenger arrival card about his criminal record.
Brisbane's Sunday Mail said border checks were so loose that people convicted of manslaughter, rape, kidnapping and robbery were allowed into Australia.
New Zealanders can travel freely to Australia provided they haven't been sentenced to a year or more in prison.
There has been a long-standing right of free travel between both countries but Australia moved to clamp down on New Zealand migration in 2001 by refusing access to some benefits and entitlements.
Key said despite the recent controversy across the Tasman about Kiwi migrants, the New Zealand Government had not detected "any push" to see a tightening in the regulations.
"We would certainly want to resist anything in that regard. That's one of the things we want to be cautious of. New Zealanders enjoy free passage to Australia and vice versa and that's something New Zealanders wouldn't want to lose."
But more data sharing between the two countries was one option.
He would also like to explore a relaxation of the rules for holidaymakers - potentially returning to the passport-free exchange that used to exist between the two countries.
A lot has already been done to free up travel through initiatives such as Smartgate.
"The question is whether there is more we can do. I have a feeling the Australians are showing a bit more interest on that side, so that's something I'm going to follow up on.
"The proposition was once put up that we get rid of passports for [travel between] Australia and New Zealand - the advice I've always had is that was very challenging to achieve."
But if Australia was "agreeable", he wanted to explore it.