The protesters gathered at the corner with Paterson Street at midday where they chanted, rang bells and displayed placards knowing Mr Gutwein would be inside, criticising the government for not adequately addressing the climate emergency.

They were also celebrating the first birthday of their dads with yarn - or DARN - group.

Shortly afterwards, Mr Gutwein and Health Minister Sarah Courtney spoke at an unrelated press conference just inside the building where the Premier was asked about the protesters.

He said he intended to give them a wave.

"To be frank, I saw them and heard them turn up. I said to the minister on the way up here: 'I'll pop out and give them a wave', and they've gone, so they're not doing too much themselves, to be frank," Mr Gutwein said.

"We are the only jurisdiction in the country that for the last three years has had net negative emissions in terms of our emissions footprint for the state.

"I would say to those protesters: go and find a [coal-powered fire station] and protest outside of that, as opposed to the climate minister's office in a state that is leading the country, and in fact is leading the world."

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He later walked to the corner to meet the group as they packed up.

Extinction Rebellion member Steve Saunders said it was positive to have a "line of communication" with Mr Gutwein, but they "agreed to disagree" when it came to old growth logging.

"We can achieve more by dialogue than by confrontation," Mr Saunders said.

"We will still continue to raise this with the public to try and get more of the public involved, because we know that politicians are highly susceptible to public opinion."

In response to the Premier's suggestion that they find a coal-powered station instead of protesting in front of his office, Mr Saunders said Tasmania was playing its role in the extinction crisis.

"We're certainly leading the world in extinctions and habitat destruction, and yet they continue to log old growth," he said.

An Extinction Rebellion member arrested and charged with failing to comply with police orders during a Launceston protest avoided a fine in the magistrates court this week, but was ordered to pay about $60 in costs.

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