Tukere, 42, died after a daylight brawl in Ngāruawāhia on December 27.
Acting Detective Inspector Andrew Saunders said in a statement police were still seeking information about the death but were following “good lines of enquiry”.
“Police have been speaking with a number of people who are helping to build a picture of what occurred leading up to Turipapa’s death.”
Police were alerted to people fighting on Waipa Esplanade, near the intersection of Newton St, about 1.30pm on December 27.
“The warrant powers have assisted in de-escalating gang tensions in the area with a number of arrests made and weapons seized,” Saunders said.
“Police have also obtained information during the execution of these warrants that may be relevant to the homicide, and this information is currently being reviewed by the investigation team.”
The warrant is due to remain in place until tomorrow, at which time it will be reviewed.
Saunders said police continue to appeal to the community and anyone who may have information relating to Tukere’s death should contact police.