Kiwis can no longer cross the Tasman and say "where's Centrelink" and Australia should not have a "whatever goes" attitude to such welfare, an Australian Government MP says.

Sharman Stone, a Liberal Coalition MP from Victoria, was on a committee that heard from Labour leader Andrew Little and MP Phil Goff this morning.

She said lobbying for greater rights for Kiwi expats' would need to be looked at, including a clearer path to citizenship.

However, New Zealand and Australia were separate countries and the sweeping changes Australia made in 2001 were not without cause.

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"Now you have to have a visa to come -- you just don't walk in the door and say, 'where's Centrelink', which used to happen, particularly for a lot of the single-supporting parents, because our welfare was higher value.

"So let's look carefully at all of those points ...[but] we are separate, sovereign nations, so we are not obliged to say, 'whatever goes'."

In a rare move, Mr Little and Mr Goff will today appear before two committees in Canberra -- the Joint Standing Committee on Migration and Joint Standing Committee on Foreign Affairs, Defence and Trade.

The primary purpose of the trip is to highlight the lack of rights for an estimated 250,000 to 350,000 Kiwis living in Australia on "non-protected" visas, including few welfare safety nets and no automatic path to permanent residency or citizenship.

Both Labour- and National-led Governments have been lobbying for change since Kiwis' rights were greatly reduced in February 2001 by John Howard's Liberal Government.

After presenting to the foreign affairs committee, of which Dr Stone is a member, Mr Little said there was "very robust discussion" with clear views expressed.

"But, in summary, I would say there was a broad acceptance that there is some unfairness in the way the rules are applied, and a willingness to look at that and make some refinements that has been in place since 2001."

There were blunter views expressed by a minority of members, Mr Little said.

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"There was an opposing view very clearly and squarely put to us. Some of the Liberal members who were there gave us a good hearing, they accepted that there was some work to be done. And we also heard the view that, if Kiwis didn't like it they could go home."

Mr Little said the discussion was not about a reversal of the changes, but there was acceptance that some tweaking could be needed -- such as a lack of access to the National Disability Insurance Scheme, which Kiwi expats' help fund through Medicare levies.

Dr Stone, who spoke to New Zealand media on her way to the committee meeting, said she was aggrieved that Australians living in New Zealand faced land-buying restrictions, apparently a reference to the Overseas Investment Office.

Her Liberal colleague, MP David Coleman, said Australians had "great affection" for New Zealanders, but the issue was not "top of mind" in Australia at present.

Labor MP and shadow Attorney-General Mark Dreyfus said most of the thousands of New Zealanders living in his South East Melbourne electorate told him they did not want Australian citizenship, because they would go back to New Zealand one day.

Mr Dreyfus said it was right for New Zealand and Australia to work towards closer economic ties, but they were separate countries.

"New Zealand declined the opportunity to join the Australian Federation when we became a country in 1901, I don't think New Zealanders are saying they want to be one country with Australia."

On comments to the Herald by Liberal senator Ian Macdonald that New Zealand could take up the chance to become a state of Australia, Mr Dreyfus said that was a decision for New Zealanders -- and he thought it would not be a favoured move.

Mr Little and Mr Goff will this afternoon meet Opposition leader Bill Shorten and deputy leader Tanya Plibersek, Labor MPs, and Australian Immigration Minister Peter Dutton.

Mr Little will talk to Mr Dutton about a new law, introduced last December, that enables the deportation of non-Australians who are sentenced cumulatively to a year or more in prison, or who are judged to fail character tests.

Riots at the Christmas Island detention centre and the arrival of criminals in New Zealand, including on the so-called 'Con Air' flight, have been a major political issue this year.

But partly because of Mr Little's Australian trip, focus is now switching to the related but wider issue of all New Zealand expat rights.

While in Manila for an Apec summit Prime Minister John Key told media that he sensed Australian Prime Minister Malcolm Turnbull could move on giving a clearer path to citizenship, as an alternative to changing the threshold at which deportations occur.

And on Monday he took a swipe at Mr Little's Canberra trip, saying it could jeopardise progress being made by the Government's quiet diplomacy.

How life has changed for New Zealanders living in Australia:

• 1994: Australia introduces special category visas for New Zealanders, classing all arrivals as temporary, albeit with the right to stay indefinitely.

New Zealanders have rights generally equivalent to permanent residents, with some waiting periods.

• February 2001: Widespread changes after New Zealand refuses to reimburse the cost of social security payments made to Kiwis.

New arrivals are classed as "non protected" visa holders, and excluded from the dole, parenting payments, youth allowance, disability support pensions, student loans and other programmes.

There is no longer a clear path to citizenship.

•December, 2014: Law change sees non-Australians sentenced to a year or more in jail, or deemed to have poor character, detained and deported. Spike in number of Kiwis held and sent to New Zealand.

•October, 2015: John Key fails to get meaningful concessions on deportation issue when new Australian Prime Minister Malcolm Turnbull visits New Zealand. On same visit student loan access for Kiwis who spent childhood in Australia announced.

This week: Key says he senses Australia could move, in the long-term, to give New Zealanders a clearer path to citizenship. Labor leader Andrew Little in Canberra to lobby politicians.