The Free Speech Coalition has filed legal action against the Auckland Council and its mayor, Phil Goff.
The proceedings come after Mr Goff's clear message that far-right advocates Lauren Southern and Stefan Molyneux should not be speaking at council venue the Bruce Mason Centre.
The speakers are best known for the contentious views on topics including gender, feminism, immigration and Islam.
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The pair's event was cancelled by venue operator Auckland Live, which cited health and safety reasons.
Free Speech Coalition member David Cumin says they presented Mr Goff with an open letter suggesting he avoid litigation costs by reopening discussions with event promoters over the potential hosting of Ms Southern and Mr Molyneux.
The action is to ensure politicians and officials don't discriminate against views they dislike, Mr Cumin says.
"Despite his earlier tweets, Mr Goff now claims it wasn't about banning the speakers because of their political views, but about safety," Mr Cumin said.
"What he risks is delivering a 'heckler's veto', where potential protesters get to decide who Aucklanders can hear from or associate with."
Auckland Council told Newshub its legal team is assessing the claims, but is unable to comment further as the matter is before the courts.
Ms Southern was originally denied access to Australia, but her visa was approved by the Home Affairs Department last week.
She told Sky News Australia the initial visa denial was due to her criticisms of Islam.
Mayor Phil Goff sent a clear message that the pair are not welcome at Auckland Council venues.
"I just think we've got no obligation at all - in a city that's multicultural, inclusive, embraces people of all faiths and ethnicities - to provide a venue for hate speech by people that want to abuse and insult others, either their faith or their ethnicity," Mr Goff told Newshub.
"These individuals who want to incite hatred against others are, in my view, not welcome here," he said.
Ms Southern was banned from entering the United Kingdom after displaying flyers reading "Allah is a Gay God" and "Allah is trans". She claims the flyers were part of a stunt proving Islam is homophobic.
Stefan Molyneux also shares his views in lengthy internet videos, including arguing race is tied to IQ and reportedly saying women are to blame for violent men because adults are informed by "dysfunctional early childhood experiences, which are all run by women".