The tsunami has reached North Cape, Raoul Island (one of the Kermadec Islands), Great Barrier Island, East Cape and Tauranga, according to GNS Science's Tsunami Gauge Network.
Far North Civil Defence controller Alastair Wells told Radio New Zealand a surge of around 20cm is expected initially, but this is forecast to build up to 1m within the next three hours.
The tsunami marine warning will remain in place until an all clear is pronounced, Mr Wells said.
Civil Defence said there was a "minor land threat" posed by the tsunami.
Based on real-time tsunami modelling and comparison with historical events, the interpretation was that a minor land threat - wave heights of just over 1m - existed in Northland between Ahipara and the Karikari Peninsula as well as in the Bay of Islands and the Chatham Islands.
A minor land threat means there is a small potential for impacts on beaches in these areas.
A marine threat remains in place for the northern North Island from Kaipara to Ahipara and south of the Karikari Peninsula to Gisborne.
Auckland Civil Defence controller Clive Manly said strong currents, disturbed seas and estuaries were expected in Auckland.
"We are working with the Harbour Master and other people with activities on the water," Mr Manly said.
Civil Defence is advising that any activities or events planned at beaches this morning should be cancelled.
People are being warned to stay out of and away from the water. Civil Defence says a tsunami comes in a series of waves and the first may not necessarily be the largest.
Civil Defence Senior Communications Advisor Adrian Prowse says the disturbed ocean currents will affect boats near the coastline.
A four-metre tsunami washed away cars and tore away buildings along Japan's eastern coast near the epicentre after the massive earthquake hit at 2.46pm yesterday (6.46pm NZST).
The death toll in Japan has reached 133, press reports said this morning.
More than 700 people have reportedly been injured and hundreds more are missing.
People in coastal areas of New Zealand are being advised to:
1. Stay off beaches.
2. Stay out of the water (sea, rivers and estuaries, including boating activities).
3. Not go sightseeing.
4. Share this information with family, neighbours and friends.
5. Listen to the radio for updates.
6. Follow instructions of your local Civil Defence authorities.
Initial waves were expected on the NZ coast at the following times:
6.23am - North Cape
7.23am - Auckland's west coast
7.29am - Gisborne
7.53am - Wellington
8.05am - Auckland's east coast
8.08am - New Plymouth
8.17am - Napier
8.37am - Westport
9.29am - Dunedin
10.03am - Lyttelton
10.15am - Nelson
10.20am - Bluff
* These times are approximate. Civil Defence advises actual arrival times may be up to an hour later than those published.
- NZ HERALD STAFF, NZPA, NEWSTALK ZB