Mr Morgan says the problem is caused by people not keeping control of their cats and letting the pets roam where they kill native wildlife.
He advocates councils making micro-chipping mandatory for cats to determine ownership, so un-owned cats could be "zipped" and any pets caught wandering could be returned for a fee. There should also be a 24-hour curfew on cats, with them only allowed out on leashes.
A less restrictive, and perhaps more practical, form of regulation for cat ownership was raised in Tauranga this week.
Representatives from ARRC (Animal Rescue and Rehabilitation Centre) Wildlife Trust - which is unlikely to share Mr Morgan's more hardline views - has asked the Tauranga City Council to consider putting a limit on the number of cats people can own. It also want owners to register and microchip their cats.
The organisation says the city has a problem with cat colonies and forcing owners to register and microchip their cats would establish a sense of ownership, helping keep numbers down.
Mayor Stuart Crosby says he is reluctant to introduce rules for registering and micro-chipping cats but I think the idea has merit and should be explored.
While it is a given that pet owners will develop strong attachments to their cats, this needs to be balanced against the need to protect our native fauna.