Across the Tasman, the sport is already banned in four Australian states.
But the Matamata man who raised Llanaprize said the sport saved more horses than it killed.
Trainer and part-owner Peter Brosnan was distraught this week when he told the Herald on Sunday about his horse.
"He came to us when he was a 2-year-old. Our horses are part of the family. It's like your cat or your dog. You're with them every day."
He said jumps saved a lot of horses from becoming pet food.
"They breed so many horses, you can't have homes for them all. Most horses that go to the jumps are too slow for the flats."
Brosnan said Llanaprize was kept out of love. He never won a race, the trainer said, and never made much money.
Brosnan said he understood the calls for a jumps ban - but Safe and the Greens were misguided. The trainer said anti-jumps activists didn't recognise the affection and care trainers had for horses. "They really need to come and see the horses and meet the people."
Brosnan said jumps racing was no more dangerous than equestrian eventing. "The percentage of horses that get hurt is minimal."
Safe campaign director Eliot Pryor said jumps racing was inherently cruel. His group was monitoring the number of horse deaths this year. "This is the side of jumps racing that is hidden and that the industry doesn't want to talk about."
Pryor said New Zealand-raised horses were dying in South Australia and Victoria, where the sport was still legal.
Green Party MP Mojo Mathers said a principle was at stake. "The bottom line is that it is unacceptable to have animals dying for our entertainment.
"I would certainly support an immediate suspension while the causes of the deaths are looked at."
Mathers said the sport in Australia was fading away. "It's becoming more unpopular with the public because of the level of suffering involved."
New Zealand Thoroughbred Racing said fatalities occurred in less than 0.1 per cent of starts. "Those involved in racing in New Zealand ... have the greatest regard for animals. It is, after all, in their interests to do so." NZTR said horse owners could spend more than $30,000 a year on a horse's training costs.
The group was working with other agencies to make the sport safer but a "zero death" policy was unrealistic. "It must be accepted that in some sports sometimes lives will be lost. It is inevitable when dealing with livestock.
"The issue is how many and at what point the numbers become unacceptable."