Four opposition MPs who left their seats as part of the haka at the end of the Treaty Principles Bill debate last month have been referred to the privileges committee.
They include Te Pāti Māori MPs Debbie Ngarewa-Packer, Rawiri Waititi, Hana-Rāwhiti Maipi-Clarke and Labour's Peeni Henare.
Speaker Gerry Brownlee said the haka was "disorderly and disruptive".
He said he was not ruling about the appropriateness of haka and its place in the tikanga of the House, which was a different matter that was to be considered by the Standing Orders committee later in the day.
Brownlee said he had received letters about the matter from NZ First Minister Shane Jones, National MP Suze Redmayne, and ACT MP Todd Stephenson.
He noted he had already "named" Hana-Rāwhiti Maipi-Clarke who led the haka, saying it should be considered a serious matter by every MP.
Photo: VNP/Louis Collins
"Taking an action to prevent votes being completed is completely unacceptable. At this point, however, naming has been the only action I've chosen to take on that matter.
"The letters I've received name a number of members who participated in a haka in the House, and in particular four members who left their seats to stand on the floor of the house, three of those members advancing towards the seats of another party. That is disorderly and cannot be considered anything other than disorderly.
"The issues of members leaving their seats to participate in an activity that was disorderly and disruptive to the procedure of the House is something that should be considered further. The House may treat as a contempt any act which obstructs or impedes the house in the performance of its functions."
He said it was therefore his decision the Privileges Committee - Parliament's watchdog which has membership from all the parties in Parliament and can hand down punishments for bad behaviour - should consider the actions of Henare, Ngarewa-Packer, Waititi and Maipi-Clarke.
He also said he had received a letter from Ayesha Verrall seeking a debate about the latest health workforce plan as not every announcement warranted an urgent debate "even though the announcement may be important".
"There must be such an element or urgency that the matter must take precedence over other business. I do think that this application reaches that threshold, the application is therefore declined."
Deborah Russell had also sought an urgent debate on the removal of humanities and social sciences from the Marsden Fund, but that received the same response.
How the haka unfolded
A haka led by Te Pāti Māori interrupted voting for the first reading of the Treaty Principles Bill last month.
Opposition MPs and the public gallery stood to perform Ka Mate, after Hauraki Waikato MP Hana-Rawhiti Maipi-Clarke stood to deliver her Te Pāti Māori's vote against the bill.
Brownlee, who had expressed his lack of patience with a number of MPs for their interjections throughout the afternoon, then suspended the sitting until the bells next rang.
The video, of Te Pāti Māori MP Hana-Rawhiti Maipi-Clarke performing 'Ka Mate', as well as her subsequent suspension from the House, was picked up widely by international media.
Te Pāti Māori co-leader Rawiri Waititi said the response to the video, particularly from indigenous peoples from other nations, had been supportive.
However, ACT leader David Seymour believed the incident had made New Zealand look bad on the world stage and that the vast majority of New Zealanders thought it looked "ridiculous".
The bill which has been promoted by Seymour has led to nationwide protests with Prime Minister Christopher Luxon himself calling it "divisive".
In its negotiations with the coalition government ACT secured a commitment to get the bill as far as committee stage, but no further.
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