New Zealanders across the Tasman, who are joining Labour MPs in their fight to be treated the same as Australian citizens, say the NZ Prime Minister hasn't accomplished much in seven years of "quiet diplomacy".
Oz Kiwi - a not-for-profit group - lobbies for New Zealanders living across the Tasman to be given the same treatment as Australian citizens, and will be joining up with senior Labour MPs from New Zealand to talk to Australian politicians this week.
Labour leader Andrew Little and his senior MP Phil Goff are travelling to Canberra to appear before two Australian select committees.
Mr Little said hundreds of thousands of New Zealanders were paying taxes in Australia, but were being unfairly excluded from benefits.
The Prime Minister has criticised the visit, saying he hoped the Labour Party did not make matters worse by lobbying Australian MPs about the treatment of New Zealanders living there.
Mr Key said the rules that excluded Kiwis were popular in Australia.
He said there could be pushback if Labour went over there and started making demands of the country's MPs.
"If he goes over there and starts telling a whole bunch of MPs that he demands change, then one of the risks is that you get more pushback, it highlights the issue which just encourages everybody else to go down another pathway."
Mr Key said working behind the scenes to bring about change was the best approach.
But Tim Gassin, the chairman of Oz Kiwi, said Mr Key had not achieved much by handling things that way.
"John Key says he has been dealing with quiet diplomacy for the past seven years, and we haven't really seen much out of that. And in some ways I'm delighted to see Andrew Little and Phil Goff come in, because there is a lot of work the New zealand government hasn't been doing.
"It's all very well for John Key to go to the Prime Minister and say, 'hey mate, we don't think this is fair', and then the Prime Minister comes back and says they're going to do nothing, which seems to be what has been going on. You need to get out there, you need to talk to the back bencher MPs."
Mr Gassin said they had made positive progress with the Labor and Green parties across the Tasman, and even in the more conservative Liberals and Nationals, although support from these parties was largely confined to the back benchers.
He said New zealanders moving to Australia were not doing so to access social security, they were going there because they had family in the country and chances for employment, but when it came to the politics of the situation, it was all an issue of money.
"The key issue here is that it costs Australia either way. If you return more social services to New Zealanders, then there is a cost to that. At the same time, you have 200,000 people living here with no political rights, no access to some basic social services, limited access to education and limits on employment opportunities. That's not a great thing for any country, and that will cost Australia."