"Education has its place, of course, but stronger enforcement is needed. That's what the public wants from us so we can tackle bad owners as well as bad animals," he said.
Criticism of how council has handed some issues and how quickly officers have responded continues and last weekend the Chronicle spoke to one Castlecliff family at their wits' end.
The family, who do not want to be identified, has been complaining since June about dogs and horses on one residential property.
"The dogs are bad enough but there's a major problem with the horses these people keep," the father said.
"Half the time the horses wander unattended around the streets and especially on the reserve on Seafront Rd. Horse droppings are all over the reserve, and the owners make no attempt to clean up the mess. That's where we try and take our family but its a mess.
"We've been into the council offices, filled out Fix-it forms but still nothing changes. Why can't the council get this sorted?"
Mr Stevens said he was aware council staff were working out "an agreed plan of attack" for this particular complaint and a resolution was not far away.
"We're tackling it collaboratively because what's been happening covers different areas. It means we've involved animal health staff, parks and reserves staff and public health staff," he said.
New provisions in the draft animal bylaw include specific provisions about keeping animals for breeding, specific conditions on keeping cats, and rules around how poultry and pigs are kept.
There are new conditions around keeping horses in the urban area, to help officers when it comes to identifying animals.
There is also a new section about beekeeping. The existing bylaw does not include specific conditions and it was left to the council officer's discretion when investigating nuisance complaints involving bees.
Council policy adviser Ceinwyn Bannister told the operations and reporting committee meeting last week the draft was part of a rolling review of council policies, and rather than changing the policy too much it expanded it in some areas.
Ms Bannister said as an example that the policy did not limit the number of cats a person could have on their property, but if they were causing a nuisance then council staff would issue an abatement notice.
"It would be determined on a case-by-case basis. But if the cats are looked after properly then it should not be an issue," she said.
Councillor Martin Visser said not capping the numbers could have an impact on native birdlife, and some other councils were limiting the number of cats.
Jonathan Barrett, council's deputy strategy and development manager, said trying to cap numbers would prove difficult because that meant officers would have find every cat.
"Then you'd have to chip them, which brings with a whole new set of work. In fact it would be a regulatory nightmare," Mr Barrett said.
The policy will be back on the council's agenda on September 8 then the draft policy will be open for public consultation until October 15.
Submissions will then be heard by the strategy and policy committee before being adopted.
The review will attempt to reflect issues which had arisen and persisted since the bylaw was first drafted in 2010.
It is also a requirement under the Local Government Act 2002.