Rebel Tasmanian Labor MP Brenton Best is refusing to walk away from his call to dump the Premier Lara Giddings.

A public rebuke from the Deputy Premier for Mr Best to shut up has emboldened the Braddon MP, who says he will not quit the party.

Mr Best has now gone a step further and said he is not the only one in caucus who is fed up with the Premier’s refusal to rule out doing another power-sharing deal with the Greens.

“There certainly is pressure within the Parliamentary Labor Party for a change of direction,” he said.

He says it is just nerves holding back other MPs from joining him.

Labor Senator and powerbroker Carol Brown sidestepped questions about whether Mr Best has support.

“There has been a lot of discussion in terms of what we need to do in terms of the state election next year,” she said.

The Senator believes Lara Giddings will lead Labor to the next state election.

Senior Liberal Senator Eric Abetz says Mr Best’s claims are more evidence that Tasmania needs a change of government.

“I don’t think he’ll be bothering Mensa for a membership form anytime soon, but if even Brenton Best can acknowledge that the Government of which he is a part is dysfunctional, then it must be bleeding obvious.”