City of Launceston councillor Andrea Dawkins moved the motion at Thursday's council meeting.

The motion was that the council lobby the state government to amend the Dog Control Act to allow greyhounds to be unleashed in designated areas, and ask the Local Government Association of Tasmania to support the motion.

It also asked the council to identify an appropriate off-leash area within the municipality, so the council would be "ahead of the pack" if the laws changed.

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Rosalie Saville, who helped lobby the state government last year to amend the muzzle laws for greyhounds, and runs the Greyhound Rehabilitation Enthusiasts Association Tasmania Facebook page, spoke at the meeting.

She said with 300 greyhounds being adopted annually the demand for greyhound-only exercise areas would continue to grow.

After the meeting, Ms Saville said the motion continued to allow the state to be on the front foot for greyhound rehabilitation. She said having nowhere specific for them to exercise diminishes their quality of life and can also be a deterrent for people to adopt retired greyhounds.

Greyhound-only areas would be for the safety of the dog, rather than because they're an unsafe breeds, she said.

At the meeting, Cr Dawkins was commended for her forward-thinking by her fellow councillors.

Her motion passed unanimously.

Councillor Karina Stojansek the community was becoming more aware of the fight for greyhounds and the high euthanasia rates, which meant more people were welcoming greyhounds into their lives.

"It seems unfair to deny the dogs the simple pleasure [of exercise], she said.

Councillor Paul Spencer was not at the meeting.