Australian Border Force has told New Zealand police that planned removals up to March 30 have been postponed. New Zealand police had then notified other agencies.
A police spokesperson said this was due to the current border restrictions "affecting the logistics of the process".
"Immigration New Zealand will continue to deport individuals where possible.
"Each deportation is considered on a case by case basis and involves an assessment of the individual's circumstance as well as New Zealand and international travel restrictions as result of Covid-19."
The police spokesperson said it might be requested to support these "interactions" but it has currently paused assisted deportations until it can secure the return of its travelling staff.
More than 2000 New Zealanders have been deported by the Australian Government under changes made to section 501 of the Migration Act in 2014.
The rules now allow Australia to eject New Zealanders on "bad character grounds", for being sentenced to 12 months or more in jail, or at the discretion of the Home Affairs Minister, all in the name of national security.
Some of the Kiwis have been in Australia for long periods of their lives, have gained permanent residency and have few links to New Zealand.
The 501 deportees were recently the subject of a stern caution from Prime Minister Jacinda Ardern to her Australian counterpart, Scott Morrison, that he didn't deport his people or his problems.
"New Zealand and Australia's relationship is being tested," Ardern said in a joint press conference in Sydney in February.
Australia was well within its rights to deport individuals who break its laws and New Zealand does the same, she said.
"But we have a simple request. Send back Kiwis, genuine Kiwis - do not deport your people and your problems."
Prime Minister Jacinda Ardern telling Australian Prime Minster Scott Morrison not to deport his people and his problems.
Ardern said the two countries did not want a "race to the bottom" on this issue but that the two leaders could reach a solution if they worked together.
