Yesterday's talks were brief, although the two leaders met later for dinner, and will meet again at the Apec summit in Bali. Their annual talks will be held in Australia next February.
Mr Abbott also said he hoped to take up an invitation from Mr Key to visit New Zealand some time next year.
"New Zealand is family in a way that no other country on Earth is," he said. "Just because we are family doesn't mean that we should take each other for granted."
But Mr Abbott was unbending on the present policies on expat Kiwis.
"New Zealanders have better access to Australia than citizens of any other country, and that's right and proper," he said. "I want everyone who comes to this country to work and pay taxes from day one and I'm delighted that this is exactly what Kiwis have done.
"So I'm happy to keep talking to Prime Minister Key and obviously to have questions from New Zealanders on this question but I'm very happy with the situation as it is right now."
Mr Key said his Government considered a free Australasian labour market "sacrosanct", giving New Zealanders and Australians the option of working in each other's country.
He said the 2001 measures had been agreed to by Helen Clark's former Labour Government and that the situation facing expats was "very firmly in Australia's court".
"While we will continue to advocate for New Zealanders ... we totally respect the sovereign right of Australia to make decisions on how they treat people who come and work in Australia."
On asylum seekers, he said that if it became necessary Australia would call on the deal reached with New Zealand, but that to stop the boats it needed to be made crystal clear that if people arrived by sea they would not go to New Zealand.