"I’m sorry for creating a misconception I was trying to trivialise it," Mr Radich said.
"It was definitely a racial slur and I do not seek to minimise it."
In a letter on behalf of the council to Mr Williams, Mr Radich had said the council was "appalled by your behaviour, which is a clear breach of the code of conduct and a serious failure to uphold the standard of behaviour expected of an elected community representative".
An investigation had been held "into your behaviour involving a racist slur towards a member of the public" and the council asked Mr Williams to consider resigning as board chairman.
Mr Radich struck a different tone in the radio interview.
"It happened in a pub and he didn’t even remember that it had happened, so it was just a relatively minor thing," he said.
"Certainly, the people who overheard the incident didn’t report it or bring it to anyone’s attention."
Word of mouth in a small community had led to the complaint, Mr Radich said.
The mayor explained his position to the Otago Daily Times.
"I remain appalled and very disappointed about what has happened," Mr Radich said.
He had been trying to present to Mr Williams a path of contrition and redemption, he said.
Mr Williams has not returned calls from the ODT, but the council said he had apologised for his actions.
Asked if Mr Williams should resign as chairman, board member Jock Frew said "that’s up to him".
Asked if she had confidence in him as chairman, board member Terina Geddes had no comment.
She also said the report by investigator Steph Dyhrberg had not been shared with board members "nor does it need to be".
The council confirmed board members would not see the report.
That was both because city councillors had the responsibility of deciding whether to uphold the findings of the investigation and in order to protect the privacy of the individuals involved, a council spokesman said.
The council voted 11-0 to accept the findings and to send Mr Williams a letter of censure.
A vote approving the content of the letter was passed 10-1. Cr Lee Vandervis voted against.