Last month, Mr Clark made headlines when he appeared on satirical news show New Zealand Today and repeated a racial slur he had drawn criticism for in 2023.
The appearance prompted councillors Ian Pottinger and Ria Bond to lodge a code of conduct complaint against the mayor.
This week, Mr Clark told Stuff he thought he was appearing on a comedy show and apologised to "anybody who felt offended".
Local Democracy Reporting approached Mr Clark after the apology, but he responded he had "no further comment to make".
Both Crs Pottinger and Bond remained tight-lipped also.
"Things are happening, so that’s all I can say."
Cr Bond was also unwilling to talk about the unfolding situation.
"We’ve still got to follow a process, so I don’t really want to comment on it at this stage, including the apology," she said.
Earlier this week, Cr Bond said an outside agency had picked up the complaint and was investigating it.
Both councillors were critical of the mayor’s television appearance at the time it aired in March, with Cr Pottinger labelling it a "train wreck".
■LDR is local body journalism co-funded by RNZ and NZ On Air.
