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Senior Sergeant Anthony Bond, of Dunedin, said the construction worker was upset about the protest disrupting traffic and delaying him from getting to a road works site.
Police arrested the man for disorderly behaviour but released him with a warning.
Hundreds of people attended a Rally for Palestine protest in Dunedin on Saturday.
The protestors were calling for an immediate ceasefire in the deadly conflict between Israel and Hamas in Gaza, which began on October 7.