The Northern Territory's Deputy Police Commissioner says an incident between police and Papunya women, who were moved on last week for dancing topless, will not be resolved with a simple apology.

ATSIC's central zone commissioner Alison Anderson complained to Northern Territory police after a group of women were moved on from a public park in Alice Springs for dancing bare-breasted.

Police have refused to offer the full details about the incident to the ABC, saying they do not want to jeopardise any investigation.

But Commissioner Bruce Wernham says local traditional owners were troubled by the performance on their land and one of the constables involved was an Arrente man who recognised their concerns.

"What we have to recognise is that there are sensitivities all around this issue and they involve obviously those to do with the ladies, who were visiting from Papunya, and also to do with the local traditional owners, who obviously have some thoughts about the manner in which ceremony happens within their country," he said.

"The important thing is that we all learn from this."

Mr Wernham says he is sorry if the Aboriginal women involved in the incident were concerned about police moving them on.

He says the local police commander is attempting to organise a meeting with the Aboriginal community and Ms Anderson so a protocol can be put in place to handle such situations in the future.

Northern Territory Chief Minister Clare Martin would not discuss police conduct, but says Aboriginal women should be free to dance topless in public.

She says there is no reason to stop the women from dancing with bare breasts.

"These are often difficult cross-cultural issues, but I would say the traditional Aboriginal women could practise their dancing in public, give the performance in public," she said.

"I think it's quite appropriate."

Cultural pride

Ms Anderson this afternoon performed a traditional dance bare-breasted with some of the women involved in the incident to demonstrate their cultural pride.

Ms Anderson danced at a cultural centre in Alice Springs with Topsy Nupaljurree and Mavis Numjemba.

Using Ms Anderson as an interpreter, the women said the Aboriginal community police officer involved in the incident falsely accused them of performing without the permission of the town's traditional owners.

"He was upset because they was performing on his country and they were really upset and they want an apology from him," Ms Anderson translated.

Ms Anderson has also indicated she is considering inviting Aboriginal women from across Australia to march topless through Alice Springs.

Land council confused

The Central Land Council's David Ross says he does not understand why anyone in Alice Springs would have a problem with the Papunya women practising in a local park.

Mr Ross says the park at Araluen is a public one and there is no reason why the women cannot use it.

"This is all brand new news to us," Mr Ross said.

"If this is the case then could that person please stand up and make it clear as to who they are and what they actually said and be very clear about that and what their rights are to this land at Araluen."