Under the laws, which came into force last Wednesday, owners of dogs which seriously injure people or animals by attacking or biting them face fines up to $4778 compared with $2389 previously.

Dog and cat owners who fail to register their pets will be fined up to $2389 - almost double the previous maximum penalty. Failing to renew registrations can cost up to $2389.

Hume Council welcomed the changed law.

"Irresponsible dog owners can affect both people and other animals, and council has long campaigned in our community to encourage responsible pet ownership," city infrastructure director Steve Crawley said.

"Registering a pet and acting to ensure that the animal is controlled and not being a nuisance or dangerous to other people or animals is the first step in the right direction.

"Hume pet owners are encouraged to know and understand how the state government's new laws will impact them."

Dogs Victoria chief executive Elizabeth White said the onus remained on ratepayers to ensure their dogs were registered and kept secure.

"Legislation has always been there, but this [new law] provides significant penalties if breached and gives more power to councils to apprehend dogs.

"We welcome it as a protection of people walking the streets with or without dogs."

Magistrates have been given new powers to order an owner guilty of an offence to attend responsible dog ownership training courses or for owners to take their dogs to obedience training courses.

From January 1 next year, registering cats and dogs will cost $1 more.

Proceeds will fund responsible pet ownership education programs, council officer training, government advisory support services for councils and animal management research.