"Dog attacks are on the rise," he added.
There were 113 attacks and 90 bites reported in January alone.
Darnell Minarapa-Brown was attacked by his uncle's pitbull in Takanini in April, just weeks before the council's announcement of the amnesty.
The 7-year-old was rushed to hospital with severe facial injuries.
He required more than 100 stitches and had a metal plate inserted into his nose and cheek.
The dog involved was surrendered to the council and euthanised.
The dog's owner said at the time that he was "shattered" by what happened to his nephew.
Council began discussions about a plan to deal with menacing dogs soon after the attack on Darnell.
Councillor Calum Penrose said the amnesty was only a "short-term solution", and called on Parliament to pass tougher laws to control dangerous dogs.
The attack on Darnell was the fourth dog attack on a child in Mr Penrose's Manurewa-Papakura ward in four weeks.
The council amnesty applied to dog breeds listed under the menacing classification in the Dog Control Act 1996.
American Pitbull terriers and pitbull-type dogs are the most common of these, although several other breeds such as the Dogo Argentino are also included.
Just under 700 dogs were registered through the amnesty scheme by June 20, but a last-minute rush saw more than 500 dog owners come forward.
From today, Auckland Council's animal management team will seize unregistered dogs and fine their owners.
