The individuals were captured on CCTV scrambling up poles in central Queenstown to remove about 30 flags in the days before the Winter Pride festival.
One appears to have a pride flag draped around his shoulders.
Otago Lakes central area commander Inspector Paula Enoka said police wanted to speak to the people pictured, or to anyone who recognised them.
"At this time we are unaware of the motivation behind this theft, and fully support this great festival that means so much to our city," she said.
Anyone with information is asked to contact police on 105 or online at police.govt.nz/use-105 using "Update Report".
The vandalism has been labelled a "deeply concerning incident" by festival organisers.
Winter Pride co-director Sam Coulthard said CCTV footage taken at 3am last Friday showed four people climbing up the flagpoles.
The street flags, worth $12,000, were installed around the Queenstown Bay and Village Green area as part of the Winter Pride event, which began on Thursday night.
