Turnbull arrived at the Auckland Airport, Radio New Zealand reported.
The talks between Turnbull and his New Zealand counterpart John Key will mainly focus on the ongoing deportation issue, with about 200 New Zealanders with criminal convictions being held in Australian detention centres waiting to be sent back home.
Key has said he will ask for special dispensation for New Zealanders but Turnbull is under pressure to remain firm.
The Australian and New Zealand Green Parties have said they will be lodging a complaint with the Australian Human Rights Commission about the detention and treatment of New Zealanders in Australia.
The New Zealand Labour Party has also said New Zealanders facing deportation in Australia are being treated unfairly and need Key to argue their case.
A small protest was held in Wellington on Friday ahead of Turnbull’s arrival.