Drew Millar, a councillor in Skye, shared images and comments from the right-wing group Britain First on Facebook earlier this month, the Highland Council Liberal Democrat group said.
An investigation was launched and Mr Millar was asked to stand aside from his position as chair of the community safety, public engagement and equalities committee.
The party said he declined to do so during the investigation but has now resigned from the Lib Dem group and the party.
Mr Millar yesterday said: “In my opinion I had done nothing wrong and had agreed to meet the complaint group.”
He said he had shared pictures of demonstrators holding “banners against freedom of speech”, adding: “I don’t think it was from Britain First.”
He said he refused to stand down during the investigation because he was “innocent until proven guilty”. He added: “I shared things that I thought people should be aware of. I was in no way, in my mind, stirring up religious hatred.”
Mr Millar also said he had shared a post describing Lib Dem leader Nick Clegg as a “cretin”, a sentiment he said he agreed with.
A statement from the Highland Council Lib Dem group said: “We were made aware that Councillor Drew Millar had shared with friends on his Facebook page images and comments which came from Britain First, an extreme right-wing organisation. This was anti-Islamic material used by Britain First to stir up religious hatred.
“In the strongest possible terms, the Liberal Democrat group condemns the dissemination of such material as utterly reprehensible and wholly unacceptable. It has no place in our free and tolerant society and any councillor, from any political party, should face swift and appropriate action when found to be in breach of stringent regulations governing the conduct of members.”
A statement from the Highland Council said: “The deputy chief executive will conduct an investigation on the basis of any evidence presented.”
Meanwhile, the deputy leader of Glasgow City Council’s SNP group has been suspended from the party after an alleged homophobic breach of the peace.
Councillor Billy McAllister, 60, was reported to the procurator fiscal in relation to an altercation with another man in the city’s Maryhill Road on 26 August.
A 47-year-old man was also reported for an alleged assault in connection with the same incident.
It is understood no-one else was involved.
Mr McAllister strongly denies the breach of the peace allegation, saying: “I will be vindicated.”
A spokeswoman for Police Scotland said: “We can confirm that a 47-year-old man was reported to the procurator fiscal for an alleged assault and a 60-year-old man for an alleged homophobic breach of the peace during an altercation which took place in Maryhill Road on 26 August.”
A SNP spokesman said: “Councillor McAllister has been suspended from the SNP group and as a member of the SNP until such time as due legal process has been completed.”