Manukau councillor Efeso Collins accused staff of racial discrimination at Tuesday night's swearing in ceremony at Auckland Town Hall.
Collins said his wife, four-year-old daughter and elders were initially told that they could not sit where they were because it was reserved for council guests. When his wife said they were guests, no-one believed them, he told Radio New Zealand.
"The fact that we don't look 'normal', and that's the problem - too many people offering the suggestion, which is essentially racially discriminatory, that brown people don't belong there.
"If I'm still being challenged like that now you can imagine what the experience of the very people I'm representing are every day when we are confronted with this type of thinking," RNZ reported.
Mayor Phil Goff told the Herald today he was incredibly concerned to hear about the incident and had passed on his concerns to Collins.
"This marred the occasion for Efeso and his family. Nobody deserves to be treated like that and if it was my family I would have been equally concerned," Goff said.
In a statment, the council's general manager of democracy services, Marguerite Delbet, said: "When Fa'anana Efeso Collins informed me of the way his family were treated at the inauguration ceremony, I was shocked and appalled."
"What happened to Cr Collins' family at this important occasion, designed to be a celebration for all the councillors and their families, is unacceptable and I have personally apologised to him and his wife on behalf of the council family.
"This behaviour does not reflect the values of Auckland Council, where diversity and inclusion are a priority and a key part of our performance plan. We are working hard to engage and build strong partnerships right across Auckland's diverse communities.
"An investigation is now underway to determine exactly what happened on Tuesday evening and how we can prevent something like this happening in the future," the statement said.
Collins' family returned to the first governing body meeting in the town hall yesterday to hear the new councillor deliver his maiden speech. They sat in the front row of the public gallery.
No-one was immediately available from the council this morning to comment on the matter.