Regional Civil Defence centres say people should be taking advice about tsunami warnings only from the national advisory centre, rather than other sources.
Civil Defence headquarters in Wellington issued an official tsunami warning just before 8am on Thursday following a 7.6-magnitude earthquake off the Kermadec Islands.
The quake occurred at 7.03am (local time), 160km east of Raoul Island at a depth of 20km, prompting a warning from the Pacific Tsunami Warning Centre in Hawaii.
Civil Defence cancelled the warning in New Zealand about 9am. When the wave eventually did hit the country's coast, it was barely noticeable.
Gisborne emergency services manager Richard Steele says there was a rise of about 20 centimetres detected at the East Cape.
Civil Defence in Gisborne and the Bay of Plenty say an issue arose when the media took took advice from the Hawaii centre instead of the national crisis management centre.
The Hawaii centre says it is now dropping the word "warning" from the alerts it sends out to countries including New Zealand because it is too alarmist and confusing.
Assistant director Stuart Weinstein says the wording of the bulletins is designed for scientists and civil defence officials who then decide what, if any, threat there is.
Dr Weinstein told Radio New Zealand's Checkpoint programme the bulletins are available to the public when they are intended to inform a country's civil defence officials and that can cause confusion.
Discussions still need to take place to decide what format the bulletins will take, he says.
Civil Defence Minister Craig Foss is satisfied that the tsunami warning in New Zealand was the correct course of action. Mr Foss says Civil Defence's messages were accurate and it is not responsible for confusing messages from other sources.
Civil Defence national controller David Coetzee says although some will argue it was an over-reaction, the threat was comparable to that posed by the 9.0-magnitude earthquake in Japan which triggered a tsunami on 11 March, and Thursday's warning was not inappropriate.
Warning to stay out of water
Civil Defence headquarters says people still should not go into the water in Northland and Hawke's Bay unless they absolutely have to as there could still be unusually strong tidal surges and currents.
It says the danger should have passed by Friday morning.
In Tonga, the National Disaster Office says some schools and businesses closed in the morning and people headed home to avoid coastal areas.
Ferries are operating and there are no significant reports of unusual waves.