Bob Smytherman, Liberal Democrat councillor for Tarring, has been criticised for displaying a poster in the "Tory Watch" of his website which uses a vulgar four-letter C-word.
Larger images of the poster as it appeared on the website (with the offending word pixilated out) can be seen by clicking on the view gallery button.
The poster pictures London mayor Boris Johnson with the Tory leader David Cameron, accompanied by a derogatory message.
"No place in politics"
However, Mr Smytherman, who has now removed the poster, said it was a "harmless cartoon" and did not believe there was any reason for him to stand down.
Conservative Tim Loughton, standing for East Worthing and Shoreham, called for an apology and said: "This sort of crude electioneering has no place in British politics and they should be ashamed of themselves."
Peter Bottomley, Tory parliamentary candidate for Worthing West, said it went "beyond the limits of acceptable campaigning" but he thought Mr Smytherman would recognise he had made a mistake.
Other Tory supporters have been more outspoken, with Worthing borough councillor for Gaisford, Bryan Turner, describing it as "vile and obscene" calling for Mr Smytherman's resignation.
Mr Smytherman's website, which is emblazoned with the Liberal Democrat logo and entitled "Bob Smytherman my councillor" and can be accessed via the Worthing Council website.
"I had an election cartoon we all know has circled around in the silly season we call elections," he said. "I had not given it much thought. As soon as somebody said they were offended about it, I took it off."
He added: "It has nothing to do with the party whatsoever. It is my personal blog. It is neither a national party or local party website."
Hazel Thorpe, the Lib Dem parliamentary candidate for Worthing West, said: "He realised it was a stupid thing. It was a joke at the time. In the current climate, it is a joke in bad taste.
A longer version of this story can be seen in the Thursday, April 15 edition of the Worthing Herald.
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I do not approve of this kind of joke."
But she added: "As my agent and fellow councillor, I still have faith in him."
James Doyle, Lib Dem parliamentary candidate for East Worthing and Shoreham, did not think Mr Smytherman's actions reflected negatively on the party.
n The Herald Says: page 20.
Lib Dem agent slammed for