The Australian government has given an undertaking that it will take weeks, not months, to process New Zealand detainees who want to go home.
NZ Justice Minister Amy Adams on Tuesday discussed the issue with Australian Immigration Minister Peter Dutton following opposition claims that it could take up to 20 weeks to repatriate a detainee.
"It was a constructive conversation with minister Dutton, making it clear that if New Zealand citizens elect to return to New Zealand then that process can generally be worked through in a matter of days, or at most weeks, not months," Ms Adams said on Tuesday night.
Mr Dutton also gave her an undertaking the detainees wouldn't bear any of the cost of travelling to New Zealand.
According to official Australian figures, there are 585 Kiwis in the deportation pipeline.
Of those, 34 were convicted of child sex offences, 22 for murder and 16 for rape or sexual assault.
About 40 New Zealanders are being held at the Christmas Island detention centre, which has just been brought under control after a riot.
In parliament on Tuesday furious Labour MPs walked out after Prime Minister John Key accused them of "backing rapists".
He had faced hostile questioning over the treatment of the Christmas Island detainees, and complaints that it was taking months to get them back when they chose to leave.
"Some of them are rapists, some of them are child molesters, some of them are murderers and these are the people the Labour Party is saying are more important to support than New Zealanders who need protecting when they come back here," he said.
Responding to further questions, he said, "well, you back the rapists".
Speaker David Carter refused to order him to apologise, and Labour MPs walked out in protest.
Australia's new immigration rules came into force in December.
Any non-citizen who has served 12 months or more in prison can be deported.
CRIMES FOR WHICH KIWIS ARE AWAITING DEPORTATION:
* Child sex offences (including pornography) - 34
* Murder (including manslaughter) - 22
* Rape, sex offences - 16
* Assault (including grievous bodily harm) - 121
* Theft, robbery (including armed), breaking and entering - 83
* Drug offences - 64
Source: Office of the New Zealand Prime Minister