Conservative Beverley Dunlop, who represents Moordown, said she received three calls from an unknown man on Wednesday night during which he threatened to decapitate her.

BCP Council said it was “very alarmed” and Dorset Police said it was trying to track the person responsible.

Cllr Dunlop was cleared of breaching the council’s code of conduct by its standards committee earlier this month after Facebook posts she made prompted a formal Islamophobia complaint.

In one of the posts, she said fundamentalists were “hiding in plain sight in the Muslim community” and that this would not change “until they are more frightened of the British government (because they and their families might get deported) than they are Isis”.

In another she said: "I hate to ban anything really but I'd suggest we start with mosques."

Cllr Dunlop said her comments had been taken out of context and that they had been “written in jest” and “removed from the surrounding discussions to fuel a political agenda”.

She was cleared of breaching the council’s code of conduct earlier this month following the completion of an independent investigation which ruled her posts had been made in a personal capacity.

Although the standards committee accepted this finding, it made no judgment on the content of her posts and called for more powers to adjudicate over councillors’ personal comments.

Following this, on Wednesday night, Cllr Dunlop said she had received three calls from a man who told her she would be decapitated.

Posting on Twitter on Thursday, she said: “Thank you to those who have gleefully and publicly defamed me following a wrongful allegation of Islamophobia.

“Special shout out to the incompetent BCP Council standards committee who kicked it off again.

“Last night a man called three times to tell me I was going to be decapitated.”

A spokesman for Dorset Police said it received a report on Thursday morning that a woman had “received malicious communications the previous evening”.

They said an investigation had been launched to try and identify the caller and that no arrests had been made.

Last year, 13 members of BCP Council said they had been targeted by abuse with almost half of them having to get police involved.

In a statement, the council said it was glad the government had recognised an “increase” in threats against councillors and that it was working with Cllr Dunlop to see what support it can offer.

“BCP Council is very alarmed to hear of the call made to Cllr Dunlop,” it said. “The chief executive has been in contact with the councillor to discuss what support the council may be able to provide her.

“[The] government has recognised the increase in threats and attacks on politicians over recent years and agreed, for example, that the personal contact details of councillors need no longer be published.

“We will be working with Cllr Dunlop and indeed all councillors to do whatever we can to assist.”

Cllr Dunlop said she did not wish to comment further about the calls while the police investigation was ongoing.