He said it was during the time of the previous Labour Government that Australia toughened its laws to reduce the support and entitlement given to New Zealanders living there.
"It is just frankly a little bit rich getting lectured by the leader of the opposition when they were the government that signed New Zealanders up to worse rates, and like a lap dog accepted it for seven years and did nothing about it."
Since 2001, Kiwis arriving in Australia have been classified as "non-protected" special visa holders, which means that, unlike permanent residents, they are not entitled to social support such as benefits and student loans.
The detention of New Zealanders in Australia - some on isolated Christmas Island near Indonesia - will be high on the agenda when Mr Turnbull makes his first international visit as Prime Minister to New Zealand this weekend.
National's coalition partners have called the Government's response lacking so far, but Mr Key has said it was important not to "badger" the Australians.
About 200 New Zealanders are currently held in seven Australian detention centres, after a new policy brought in late last year to detain and deport non-Australians who have incurred a prison sentence of a year or more.
There could be up to 1000 New Zealanders who could eventually face deportation from Australia.
Mr Turnbull and his wife Lucy will join Mr Key and Bronagh for a private dinner on Friday evening, ahead of a bilateral meeting between the two prime ministers on Saturday.
Last month Justice Minister Amy Adams announced the signing of a new information-sharing agreement with Australia, which would provide more details on criminals being sent to New Zealand, including a summary of offences, case history, fingerprints and photographs.
At the time, Ms Adams said the next step was to change the law to ensure offenders who arrive here were subject to the same oversight as they would have been if they served their prison sentence in New Zealand.
The Herald has documented the cases of some New Zealanders detained in Australia, including one man who was held in a police cell, where lights were left on around the clock, for nearly three weeks before being shifted to a detention centre.