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People in New Zealand are being urged to stay off beaches, and stay out of the sea, rivers and estuaries and to avoiding going sightseeing.
The Ministry of Civil Defence and Emergency Management (MCDEM) said preliminary modelling suggests waves of between 0.2 and 1 metre high would arrive in New Zealand between 6pm and 7pm tonight.
Civil Defence New Zealand issued a tsunami potential threat advisory for many coastal parts of New Zealand including Dunedin and the Clutha District but this has now been downgraded.
A wave between 0.2m and 1m may occur, and was expected to reach the South area between 8pm and 9pm today.
Clutha District Civil Defence staff are on stand-by.
Dunedin City Council civil defence staff say they are not expecting any damage in Dunedin.
As at 4pm today the largest tsunami impact reported was a 90cm wave in the Solomon Islands.
DCC Defence Emergency Management "will continue to monitor the expected risk levels and will communicate any indication of an on-shore risk".
Emergency services on Santa Cruz island have confirmed the tsunami has destroyed three villages on the island. Four villages have been destroyed in the Lata area, Andrew Catford of World Vision told TVNZ.
APNZ contacts in Fiji said Suva was blocked with traffic jams as people tried to move to higher ground.
The Fiji Ministry of Information issued a public warning this afternoon telling all residents in low lying areas to evacuate to high ground for safety.
"Schools in coastal areas are advised to release students and to ensure their safety. School authorities around the country must determine whether students are safe to remain in school - this is especially important for students that live in coastal areas,'' said the warning.
Fiji has issued a tsunami warning for the whole of the country.
The potential threat advisory will remain in effect until it is either upgraded to a tsunami warning or a cancellation message is issued, it said.
The epicentre of the powerful quake was 347km east of Kira Kira in the Solomon Islands today at a depth of only 5.8km.
The Pacific Tsunami Warning Centre said the earthquake had "the potential to generate a destructive tsunami that can strike coastlines near the epicentre within minutes''.
A tsunami warning was in effect for the Solomon Islands, Vanuatu, Nauru, Papua New Guinea, Tuvalu, New Caledonia, Kosrae, Fiji, Kiribati, Wallis and Futuna.
Editor of the Solomon Star, Ofani Eremae, said reporters had spoken to people on the ground in remote areas and they confirmed big waves have already hit their shores.
The quake was not felt in Honiara because they were so far away from the epicentre, he said.
Sirens also sounded in Fiji's capital, Suva, an indication that people were being urged to stay inside or go to higher ground.
Residents in Suva said they had been issued with an estimated time of arrival of a tsunami of 4.05pm (5.05pm NZT) this afternoon.
A Ministry of Foreign Affairs and Trade spokeswoman said the ministry was aware of the tsunami watch alert in place for much of the Pacific.
"Our Posts are monitoring the situation and the High Commission in the Solomon Islands has issued an advisory to New Zealanders registered with us as being there on [the] safetravel website.''
MCDEM is advising people to listen to the radio and television for further assessment and updates, and follow instructions of their local Civil Defence authorities.
Locals in the Solomons capital Honiara, 580 kilometres from the epicentre, said the quake was not felt there, but some villages were destroyed, according to a hospital director.
"The information we are getting is that some villages west and south of Lata along the coast have been destroyed, although we cannot confirm this yet,'' the director at Lata Hospital on the main Santa Cruz island of Ndende, told AFP.
A staff member at the Solomons National Disaster Management Office said officials were concerned about the eastern province of Temotu.
"That's the province, which if it is going to have an effect, then they will be the first people to be impacted,'' the official, who did not wish to be named, told AFP.
"They felt the quake.''