Coun Dominic Peacock was responding to the latest call - this time from East Riding Council chief excutive Nigel Pearson - to step down.
Last month the councillor, who represents Minster and Woodmansey, was found to have breached the council’s code of conduct by posting on Facebook that he had “just donated the steam of my p***” to Ms Cox’s memorial fund.
Mr Pearson’s letter followed a full council meeting which accepted December’s scrutiny committee’s recommendations that he be asked to quit.
Coun Peacock has already received a police caution and been expelled for four years from the Conservative Party.
However the unaffiliated Independent councillor, who represents Minster and Woodmansey ward, wrote back saying he had “absolutely no intention of resigning whatsoever.”
He added: “Everyone has bumped their self-righteous gums for long enough.
“I have had overwhelming support from my Ward residents with no end of ordinary people saying to me “don’t you dare resign.”
“They are the only people I listen to now.”
He told the Yorkshire Post today he would be “keeping his powder dry” as to whether he would restand at the next election and said he’s doing what he is paid to do as a ward councillor, adding: “If people still don’t like it they can get stuffed.”
One of his main critics has been Beverley and Holderness Labour Party spokesman George McManus who has described him as an “odious individual” and called on him to resign.
Coun Peacock said: “George McManus is like a turkey voting for Christmas. If I stood down there would be a by-election and there would only be one winner and that would be UKIP and Labour would be stuffed out of sight.”
He went on: “I apologised straight away (for the remark) and I am not stoking the flames on that.
“It is a closed book, I am not going back there.
“If people still don’t like it they can get stuffed.”
Independent councillor Andy Strangeway said today: “I think the man is delusional. I believe he is bringing the council into disrepute, he has clearly bought the Conservatives into disrepute and he is now bringing our residents into disrepute.”