Mr Mitchell informed Glamorgan Spring Bay mayor Debbie Wisby this week that Labor would not be honouring the $6.1 million grant the Nationals had committed to give the council for key infrastructure projects.

Cr Wisby emailed Mr Mitchell's media adviser about 3.50pm on Thursday evening, attaching a draft council media release stating that she was "extremely disappointed" that Labor had refused to honour the grant. She asked the adviser to inform her by 5pm whether Labor's position had changed.

Roughly an hour later, the mayor received a call she described as "demeaning".

"[The staffer] said, 'It's two weeks from [the] election and you're putting this out ... There's going to be consequences'," Cr Wisby said.

"They said they would lobby hard against me.

"They will ensure that my constituents know that I've lost them money."

Cr Wisby said the Labor staffer threatened to renege on a $1 million drought assistance grant promised to the community due to her comments in the draft media release about being "extremely disappointed" at Labor's decision.

"The words that he was using, basically the purpose of the call was to intimidate and I was absolutely appalled because he was holding the community to ransom," she said.

Mr Mitchell said he had called Cr Wisby to apologise "unreservedly".

"I was very upset when I learned what had happened," he said.

"I have given her an undertaking that this will never ever happen again.

"There is no place whatsoever in politics for threats and intimidation. Mayor Wisby was well within her rights to be upset."

Mr Mitchell said he had been told the interstate staffer who made the call had been "counselled".

Local Government Association of Tasmania chief executive Katrena Stephenson said she was unable to provide comment on the specific matter raised by Cr Wisby but added that LGAT was "disappointed" that funding to councils in Tasmania had been "caught up in political game-playing".

"We believe that recent community development grants should be honoured by an incoming government, particularly in light of the fact that there is a fully [funded] allocation in the current budget," Ms Stephenson said.

"This funding is important and will deliver significant benefits to communities.

"They are robust projects, shovel-ready but would not be able to be easily funded by councils."

Liberal Senator Jonathon Duniam was outraged that a "foot soldier and thug" had intimidated the mayor and said it was Labor culture to bully people.

"Brian Mitchell has sent out individuals to bully the local mayor into silence," he said.

"It's outrageous that a member of parliament, instead of engaging with his community, decides to bully a mayor via a third party into silence and submission."

Senator Duniam said Labor Leader Bill Shorten should "admonish Brian Mitchell for his bully boy tactics".