Ian Brookfield said he received threats after a video was put on Facebook showing him stopping outside the house of Tory candidate Matt Powis while campaigning on the Akron Gate estate in Low Hill.
In the footage Mr Brookfield, who is accompanied by other councillors, tells Mr Powis the Tories will “never win” in Low Hill and questions him for wanting to work across party affiliations.
The clip, which Mr Powis filmed on his doorbell camera and put on Facebook, has been viewed more than 20,000 times.
Mr Powis, the Conservative candidate for Bushbury South and Low Hill, has accused Mr Brookfield of trying to intimidate him and says he has reported the incident to the council's returning officer.
Meanwhile Mr Brookfield, who is standing against Mr Powis after moving across from Fallings Park, says he has been in contact with the police after receiving threats of violence since the clip was put up.
Mr Powis said: “I am shocked and appalled at Ian Brookfield’s behaviour. To mock and intimidate an opposition candidate outside their own home is a new low.
“The right thing for Mr Brookfield to do now is apologise for his behaviour. The video is there for everyone to see, and I’ve had huge levels of support from people right across the city.”
Mr Brookfield claimed Mr Powis has uploaded an edited version of the video that did not tell the full story.
He told the Express & Star: "It is not often that I would call someone a liar, but in this case I'll make the exception. I am more than happy for people to look at the full video and see how pleasant a discussion we had.
"If he had felt in any way threatened the he could have shut his door. What worries me are the violent threats from his family and his friends, and I have had to take action."
In the video Mr Brookfield says of Mr Powis: “He doesn’t believe in politics, he wants everyone to come together and be friends. Well, it’s not going to happen.”
He goes on to ask the Tory candidate: “Who have you upset? Why have they put you in this area on your first go [at standing for election]?” He adds: “You’ll never [win] this area. This is Low Hill."
Mr Brookfield initially responded to the claims in a series of comments on the post on Facebook.
He said the full unedited video shows he “never once bullied or harassed” Mr Powis or his family and that “at no point” was he disrespectful.
He posted: “I don’t know who in his party has got to him and made him put this innocuous video up, but if that is the level of the man then he’s better sticking to the day job. Disappointed to say the least.”