WELLINGTON, New Zealand — Omaui, an idyllic coastal town on the South Island of New Zealand that overflows with rare bird species, is home to just 35 people and seven or eight much-loved cats.

But a new proposal to phase out felines to preserve native wildlife susceptible to predators has raised the hackles of some cat-loving residents. Among other things, they worry rodents will breed out of control.

“We’re not supporting feral cats, but there are people who have doubts here about the plan,” said Terry Dean, 75, a longtime resident.

The proposed ban would impose a sunset clause for cats in Omaui, meaning that once a cat died, its owners would not be allowed to replace it. If the policy is approved, cat owners will have six months to register existing cats with the regional council and have them microchipped and neutered.