Hundreds of New Zealand plane passengers started arriving in Sydney as part of a new trans-Tasman travel bubble amid a rapidly falling growth rate in cases at the epicentre of Australia's coronavirus outbreak.

In a tentative re-opening to international tourism, travellers on the approved flights won't be required to quarantine in Sydney, authorities said.

The arrangements, however, are not yet reciprocal, with New Zealand requiring arrivals to be quarantined for two weeks under supervision at the cost of $2,045 for the first person and more for additional family members, Reuters reported.

Around 90 per cent of those travelling with Air New Zealand are booked to travel one-way, the airline said.