The incident occurred at Tuesday’s Dunedin City Council meeting, as Mr Cull attempted to halt personal criticism of his performance as mayor by Port Chalmers resident Stu Debenham.
Mr Debenham was speaking at the meeting’s public forum, but refused to be silenced, prompting the comment from Mr Cull which drew gasps from the audience.
Mr Cull, in a written statement yesterday, reiterated his earlier apology at the meeting and said he regretted "that I let frustration get the better of me".
"As someone with hearing difficulties myself, I particularly regret any offence caused to people with hearing impairments."
The council’s code of conduct required Mr Cull and his councillors to "treat members of the public in a courteous manner".
Council staff confirmed late yesterday no complaint alleging a breach of the code had been received.
However, councillors contacted yesterday said none was justified as Mr Cull had been provoked.
Cr David Benson-Pope said Mr Debenham’s presentation had been "extraordinarily inappropriate" and it was "most unfortunate the mayor was put in the position he was".
"I don’t condone the comment he made, but he did apologise for that."
Cr Mike Lord said he was "not that concerned" by the mayor’s comments, and might have done the same.
"I believe the title of the mayor is worthy of respect," he said.
Cr Rachel Elder said Mr Cull appeared to have caught "a bit of foot-in-mouth disease", but clearly regretted his actions.
The council wanted public participation, and "grizzles" were part of the process, but respectful behaviour was needed on both sides.
Cr Christine Garey said there had been "extreme provocation'' by Mr Debenham, putting Mr Cull in a "totally impossible position''.
As chairman, he had to hear a point of order by Cr Kate Wilson, who wanted to raise concerns about Mr Debenham's comments, but Mr Debenham "just carried on''.
Mr Cull was right to apologise, but "it's just not OK for members of the public to come into that situation and have a crack'', Cr Garey said.
Cr Doug Hall agreed, saying Mr Debenham was "totally out of order''.
"I've got no problem the way he [Mr Cull] reacted.
Other councillors did not return calls, while Cr Lee Vandervis said he did not think he could "usefully add anything''.
Mr Cull, in his statement, said public forum speakers could not personally attack elected members or staff, who had no opportunity to rebut criticism, or correct facts, "before they gain public currency''.
"As chair of the meeting, I had repeatedly asked Mr Debenham to stop his personal criticisms, which I'd be obliged to do whomever such remarks were aimed at.''