A councillor has been referred to police over social media posts in which racist comments were made.
A Facebook account apparently operated by Richard Alderman also called for the prime minister to be hanged for treason.
Last week Mr Alderman, an independent, won the Oakham South West by-election on Rutland County Council.
The Tory-led authority said it had referred the matter to its monitoring officer and to Leicestershire Police.
The BBC has approached Mr Alderman for a comment.
Leicestershire Police has arrested a 72-year-old man over "a number of comments made on social media" but have refused to confirm whether it relates to this case.
The force said the man, from Oakham, has since been released under investigation.
Posts made on the account have called for Labour to ban black candidates from some elections, as well as making death threats against some MPs.
Some of the abusive posts name Anna Soubry, Conservative MP for Broxtowe, and Labour's Shadow Home Secretary Diane Abbott.
Ms Soubry, a prominent pro-EU MP, has previously spoken about death and rape threats she has received.
The Stamford Mercury has reported that Mr Alderman defended a post referring to Ms Abbott as a "monkey", claiming she is "very, very racist".
Oliver Hemsley, leader of Rutland County Council, said: "We wholly condemn the use of racist and bigoted behaviour.
"This is not acceptable in our communities or our council."
Councillor Marc Oxley, leader of the council's Independent Group, said said he was "disgusted" to read the comments and "wholly supports the action" taken by the county council.
Mr Oxley said Mr Alderman was not affiliated with the group.
A spokesman for Leicestershire Police said it had been "made aware" of the comments "that appear to be of a racist and malicious nature", and was investigating the posts.