It receives no funding to help people arriving in New Zealand who have been deported from Australia after completing prison sentences.
Until recently it could cope with helping such arrivals, but not now - it has helped about 32 newly-arrived Australian deportees in the past three months, compared to around 60 in the 12 months before that.
PARS staff will meet the deportee at the airport, and help the person sign up to bank accounts, benefits, an IRD account and arrange immediate accommodation. That support is ongoing.
Asked why better funding was not available now, Mr Key said there had not been the number of deportees arriving.
Much hinges on whether Mr Key can successfully lobby Australian Prime Minister Malcolm Turnbull on the issue this weekend.
Mr Key will ask for the threshold at which a person is deported to be lowered in recognition of the special transtasman relationship, and said he will point out how much New Zealanders living in Australia contributed.
"As a group we are more employed as Australians as a group, we earn more than average Australians as a group, we are actually incarcerated at a lower rate than Australians as a group. New Zealanders are lifters in Australia, they are not leaners."
Mr Turnbull choosing New Zealand as his first international visit as Prime Minister showed that he valued the relationship, Mr Key said.
"It's a relationship that spans everything from our time on the battlefields of places like at Gallipoli, right through to economic integration between the two countries.
"Kevin Rudd in the entire time he was Prime Minister never came to New Zealand. I think the fact he is coming and he is coming here at a time where he knows there are some issues of concern to New Zealand shows that he takes the relationship very seriously."
About 200 New Zealanders are currently held in seven Australian detention centres, including on isolated Christmas Island, after a policy change last December to detain and deport non-Australians who have incurred a prison sentence of a year or more.
Labour has criticised the Government as much too slow to both lobby Australia on the issue, and to act on how to deal with the influx of criminals being deported to New Zealand.
Last month Justice Minister Amy Adams announced the signing of an information-sharing agreement with Australia that would provide more details on criminals being sent to New Zealand.
At the time, Ms Adams said the next step was to change the law to ensure prisoners arriving here would be subject to the same controls and supervision as they would be if they had served their sentence in New Zealand.