It has yet to decide what will be done if he does not apologise.
The council also asked for Cr Vandervis to commit to attendance of the council's Te Pae Māori forum.
Consideration of sanctions - should an apology not be forthcoming - was postponed pending legal advice about options for the council.
Cr Vandervis was found to have materially breached the council's code of conduct over an email he sent on July 16 last year, non-attendance of Te Pae Māori meetings and for referring to council committee mana whenua members as anti-democratic and race-based representation.
Councillors at a city council meeting today decried racism and what they described as a disrespectful attitude from Cr Vandervis, or prejudice.
The council's resolution, which included the request for an apology, was passed unanimously.
Cr Vandervis did not attend the meeting, as he is overseas, and the councillor who lodged a complaint about his behaviour, Marie Laufiso, sat back from the discussion and the vote.
Dunedin Mayor Jules Radich said he had called for Cr Vandervis to be more professional and less inflammatory.
Cr Vandervis had a long history of code breaches and there was a pattern to his behaviour, the mayor said.
Requesting an apology allowed for the "possibility of redemption".
Cr Christine Garey said Cr Vandervis had been found to have brought the council into disrepute and he had a long history of making racist comments.
There had been no self-reflection or remorse, she said.
He had emboldened other people to make racist comments, she said.
Cr Sophie Barker said if Cr Vandervis did not apologise, she did not believe he was fit to be chairman of a council committee.
Cr Vandervis chairs the finance and council-controlled organisations committee.
Cr David Benson-Pope responded to a comment from the mayor about it being worthwhile to have a range of views around the council table.
"It's not about diversity at the table," Cr Benson-Pope said.
"It's about prejudice and bigotry."
Cr Steve Walker said investigator Jordan Boyle's report for the council was fair and clear.
The council accepted Mr Boyle's finding Cr Vandervis had materially breached the code.
Cr Brent Weatherall voted for the resolution, but he also criticised the complaint delving into pronunciation of the word Māori.
Cr Jim O'Malley said casual racism could not be allowed to stand.
He would be "looking for an opportunity" to have Cr Vandervis replaced in his chairmanship role.
"What century is he operating in?"
A statement from Cr Vandervis was read out at the meeting.
He rejected accusations of racism.
"I vow to continue to exercise my right to free speech in the public interest and to be part of the diversity necessary for democratic representation on the Dunedin City Council.”
