"We're aiming to remove any cost barrier that might prevent dog owners from doing the responsible thing and having their dog de-sexed - which in turn ensures the dog is less likely to roam, bite and fight, and helps make our kids and communities a lot safer."
She said council hoped to offer this service to at least 100 dog owners, "but if it's really popular, we have the ability to fund many more".
In 2016 there were 98 recorded dog attacks on people or other animals in Napier - many of the attacks on children.
The annual report notes 69 complaints were received in the 2015/16 year about dog attacks on animals or poultry, and 29 complaints received about attacks on people.
This was down from a total 120 complaints the year before.
The council stated the particular breeds responsible for the attacks were not known, but it was important to encourage dog owners of higher-risk breeds to protect themselves and their friends and neighbours.
The programme - which runs until May - has been dubbed "Operation Underdog" and is expected to cost around $17,500, funded by a Ministry of Internal Affairs grant.
Council staff will be out on the streets, and calling into homes "of those who could benefit from the programme".
Any unregistered, classified dogs will be registered and a voucher issued for free micro-chipping and neutering at Carlyle Vet Clinic. Promotional activity will include a public information meeting, advertising, posters, and social media.
"We'll also be working closely with the SPCA, Housing New Zealand and other local agencies to spread the word on the programme," Ms Brereton said.
The council's annual dog control report was adopted earlier this month. It showed overall improvements in dog control statistics, including a decrease in the overall number of dog complaints received, from 3089 in 2014/15 to 2718.
The only complaints to increase were about roaming dogs.
It noted the number of dogs impounded had decreased by 343 since 2014/15, with a larger per cent of those impounded returned to their owner.
The number of dogs euthanised decreased from 179 to 78. More dogs were being registered and fewer infringement notices were being issued.
-To take up the offer, go to the Napier City Council reception, off Hastings Street, and register your dog free of charge before 31 May 2017.