Police were called to a Corbett St property, in Green Island, shortly after 10am, after reports from concerned residents who had heard gunshots.
Acting Senior Sergeant Tania Baron said the dogs, which had been reported as missing, were earlier reportedly seen disturbing cattle and sheep, and Dunedin City Council (DCC) animal control was advised.
DCC senior animal control officer Jim Pryde said a farmer required assistance in controlling the dogs, which had killed a lamb on his property.
"They chased another mob of sheep but at that stage it is unsure whether there are any other injuries or deaths."
Mr Pryde said the first approach by animal control officers was to catch the dogs, but when that was unsuccessful "we had to revert to the destruction of them".
"They wouldn't come to any call to be caught, and were too interested in the other animals. That is why the decision was made to destroy them.
"If they were to get away from where they were, who knows what they may lead to, because once dogs start on that crusade it is very hard to stop them."
He confirmed the dogs were registered, and came from a nearby property.
"It is also the naivety of the dog owners who don't understand what their dogs are capable of ... when dogs get into a frenzy like that and stock start running in something that started as a game."
The incident served as a reminder for dog owners to have their dogs "supervised and secured", he said.
