Te Papa is deciding whether to pull the plug on a conference being held at Wellington convention centre, Tākina, over concerns the content is hostile to trans people.
The event on Saturday has been organised by Inflection Point NZ to stop what it calls "gender indoctrination and medicalisation" of children.
Speakers at the event include Brian Tamaki, former National Party MP Simon O'Connor, as well as others from overseas.
Te Papa, who manages the space, said it was actively monitoring the situation and reviewing the health and safety and security arrangements to assess whether the event could occur safely.
It said it was aware a protest was being planned against the event "because of concerns that its content and speakers are hostile to trans people".
The police said it was also aware of it and would monitor and respond to incidents as required.
"Police recognise the right to peaceful protest, but also the right of the general public to go about their normal activities safely."
RNZ has approached Inflection Point NZ for comment, and contacted the person listed as hosting its website.
Mayor Tory Whanau said she was deeply concerned the rhetoric being discussed at the event would be harmful to the trans and queer community.
"Make no mistake, I completely and utterly condemn hate against our rainbow whānau anywhere in Aotearoa," Whanau said.
"In this city, discrimination will never be tolerated. Pōneke is a place where everyone can live with dignity, equality, and respect. End of story."
Pōneke Anti-Fascist Coalition said it had not called for the event to be cancelled, and would hold a trans solidarity event with Queer Endurance in Defiance this weekend whether the event went ahead or not.
It said it was not a safety threat and had held many successful peaceful protests over the years and intended to continue to do so.
Wellington City councillor Nīkau Wi Neera said the council owned the Tākina building.
He said ratepayer-funded spaces must be inclusive and safe for all - and he was concerned at what he called the "inflammatory nature" of the event.
He said the summit was unwelcome in the city.
The NZ Bill of Rights Act states public venues, such as those owned by a city council, cannot cancel or refuse an event because they do not support it or agree with the views of the organisers.
However, that may sometimes be superseded by factors such as competing rights and genuine health and safety concerns.
Inflection Point NZ said on social media platform X that they were not going to tolerate left-leaning politicians "acting like some kind of totalitarian regime that will cancel or shut down anyone else's opinion that they don't agree with".
The group said it would also have security in place and police would be in attendance.