Prime Minister Malcolm Turnbull has added his weight to Liberal criticism of an independent candidate for Braddon who may have a key role in the result of the knife-edge by-election later this month.
Craig Garland is running in the northwest Tasmanian seat and has indicated he'll preference the Greens and Labor ahead of Liberal Brett Whiteley at the July 28 poll - something that may secure Labor's Justine Keay victory.
It was revealed this week Mr Garland pleaded guilty in 1994 to an assault charge stemming from an incident in which a female police officer broke her wrist.
Liberal Senator Eric Abetz has questioned Mr Garland's suitability as a candidate, and was on Friday followed by the prime minister.
Mr Turnbull, who announced a $3.9 billion national agriculture jobs package on a visit to Stanley, said the charges were a "grave matter".
"Let me say firstly, violence against women, violence against police can never be accepted and must always be condemned," he told reporters.
"I think the voters of Braddon have got to weigh that up when they assess the candidates."
Mr Garland, a local fisherman, received nearly 2000 primary votes at the March state election - the most of any Braddon candidate outside the two major parties.
Advocating fishery protections, he intends to preference the Shooters, Fishers and Farmers, the Greens and then Labor.
Recent ReachTel polling shows the Liberals have a 42.9 per cent to 36.3 per cent primary-vote lead over Labor.
But the flow of preferences is expected to made it a tight race.
Mr Garland has told media that police dropped 14 charges against him over the 1994 Geelong scuffle in which he was defending his mates.
He pleaded guilty to one charge.
Labor has made fishing the focus of recent campaigning, including a pledge to ban supertrawlers from Tasmania's small pelagic fishery.
