Dog owners will also be able to get their dogs de-sexed, microchipped and muzzled for $25.
After July 1, the council's animal management team will conduct a widespread enforcement campaign.
Councillor Calum Penrose, Chair of the Regulatory and Bylaws Committee, said the recent spate of attacks highlighted the need for action and Auckland Council was best placed to take the lead to reduce harm in vulnerable communities.
"A dog attack affects an entire community. It leaves victims with permanent scars, both physically and emotionally, and can tear families apart.
"However, we recognise that this amnesty is a short-term solution and we cannot do this alone. We are calling on the support of the Government to make changes to the Dog Control Act to require all councils throughout New Zealand to tackle this issue.
"I'd like to see the Act amended to include the compulsory de-sexing of menacing dogs unless lineage can be proven, the certification of owners of menacing dogs and a formal definition of an American pit bull," Mr Penrose said.
The call for change was echoed by Mayor Len Brown, who said stronger legislation would help to reduce the harm communities in Auckland faced every day.
"Working alongside the Government will allow us to tackle this very important issue head on. In the long-term, it will reduce the strain on our resources and on the health system."
Auckland Council's Manager Animal Management, Geoff Keber, said in Auckland, pit bulls and their crosses were 20 times more likely than any other breed to be involved in a serious attack.
"We also know that dog attacks in the region are on the rise. In November 2014, there were 58 recorded attacks and 55 bites, however by January of this year, those numbers reached an all-time high, with 113 attacks and 90 bites recorded."
Mr Keber said there was also an over representation of dog attacks in some areas of the region, particularly in the south.
"While this offer is open to everyone across the region, we will be reaching out and focusing our efforts on those communities that are most at risk," he said.
Over the coming weeks, Aucklanders will see advertising and information distributed in different languages. A direct contact number (0800 462 685) has also been established for people to find out more about how they can take up the offer. People can also phone this number for emergency response in the wake of an attack.
For more information about the amnesty visit aucklandcouncil.govt.nz
