"Too early to see full wave cycle for exact wave height. GNS and MCDEM will keep monitoring tidal gauges, follow us for regular updates."
Civil Defence stressed that people should stay off beaches.
A tsunami warning for marine and beach areas was issued late last night.
The 8.2 magnitude earthquake struck off the southern coast of Mexico in the state of Chiapas about 5pm yesterday New Zealand time has triggered the tsunami warning alerts.
That warning is in effect for the Chatham Islands, Pegasus Bay, the northern coasts of Hawke's Bay, and East Cape.
There is no land threat and evacuation is not necessary.
A spokesperson for Tairawhiti Civil Defence said they have received reports from Gisborne locals this morning that the ocean appeared flat and calm.
However, she said it was important people kept off beaches while the warning was in place as the surges could get stronger.
Matthew Campbell, a cook at Hicks Bay Motel and Lodge in Hicks Bay, a coastal area on the East Cape, said the tide was very high this morning.
He said the water was calm but a strong northwesterly gale was battering the area.
The motel is one of Civil Defence's emergency evacuation spots because of its location on a cliff high above the water, Campbell said.
Although initially saying there was no threat to New Zealand, Civil Defence issued a beach and marine tsunami threat warning late last night.
Read more:
• 103 New Zealanders caught up in Mexico following strong earthquake
• Mexico earthquake: Reports of extensive, widespread damage after magnitude 8 quake
Strong currents were expected to continue for 24 hours with "tsunami activity" expected at 7am today, Civil Defence said in a statement.
Tairawhiti Civil Defence also issued a statement saying it had been advised of a "beach and marine threat" for the East Coast from Hicks Bay to Hawke's Bay, with strong currents and surges that could continue until midnight tonight.
They tsunami activity could possibly hit later than 7am and the first of it may not be the most significant. Waves of between 20cm and 1m were also possible.
"This means that unusually strong and hazardous currents and unpredictable surges are expected near beaches in harbours and estuaries," the statement read.
"The severity of currents and surges will vary within a particular coastal area and over the period this warning is in effect.
"Current assessments indicate that coastal inundation (flooding of land areas near the shore) is not expected but this assessment may change."
National Civil Defence said late last night that, "while initial assessment was that there was no tsunami threat we are now advised after further modelling that a beach and marine threat exists for the above areas.
"Unusually strong and hazardous currents and unpredictable surges are expected near the shore. This means a threat to beach, harbour, estuary and small boat activities.
"The severity currents and surges will vary within a particular coastal area and over the period this warning is in effect."
People in coastal areas are asked to stay out of the water, stay off beaches, share information with family and friends, and keep an eye out for updates.
