Efforts by authorities in Dunedin to evict protesters from the central city have so far been unsuccessful.
About 25 Occupy Dunedin protesters have been camping in the city's main public space the Octagon for 19 days.
Other protesters are occupying sites in Auckland, Wellington and Christchurch, also campaigning against wealth inequality and corporate bailout.
Dunedin City Council is the first local authority to take action to move the protesters.
The council issued a trespass order valid from 8pm on Tuesday but protesters remained in the Octagon on Wednesday morning.
Police say they will not be rushed into enforcing the trespass order because it is not a straightforward matter and requires careful consideration.
Auckland Council says it has no immediate plans to follow Dunedin's lead.
About 100 people have camped in Aotea Square with tents and a makeshift kitchen for more than two weeks.
Auckland council says officers are meeting with the protesters each day, trying to negotiate their departure as soon as possible.
It says the occupiers are breaking a local bylaw but it has no plans to force them out.
In Christchurch, protesters occupying Hagley Park say the city council has not asked them to leave.