Her death was announced this week, with Gayford and Ardern encouraging Kiwis to donate and "be kind" to the SPCA, reportedly leading to six times the usual donations being received.
Gayford thanked New Zealanders for donating to the SPCA following Paddles' death.
"It's been so wonderful to see a spike in the donations to the SPCA. It's been a little bit of good that's come from this. They do such great work," he said.
He said she had been rushed to the vet by a "really nice" neighbour who had received a knock at the door by the person who had hit Paddles.
However there was nothing the vet could do.
Gayford said the driver of the car was "very, very upset."
"I felt really sorry for him. These things happen."
The driver of the car reportedly came forward to Newshub, claiming he was "horrified" by the accident.
He said Paddles had run across the road in front of his car.
"I just almost threw up," he reportedly said after realising he'd killed the Prime Minister's cat.
The death prompted an outpouring of public sympathy, and was reported overseas by the likes of the Guardian and the Sydney Morning Herald.