The New Zealand High Commission says the damage is centred along the western coast, where there are many resorts, and the waterfront of the capital, Nuku'alofa.
A thick layer of ash remains blanketed over the capital.
Authorities are working to establish communication with smaller islands "as a matter of priority", the commission said.
The Defence Force carried out a surveillance flight of the islands today. Plans are underway for a humanitarian relief flight when conditions allow.
Early data from Tonga's violent volcanic eruption suggests it is the biggest since Mount Pinatubo in the Philippines 30 years ago, volcanologist Shane Cronin says.[break]
The eruption of the underwater Hunga Tonga-Hunga Haʻapai volcano, about 65km north of Nuku'alofa, on Saturday shot thick ash and steam 20km skywards.
University of Auckland volcanologist Professor Shane Cronin said scenes on the ground would have appeared apocalyptic after the eruption: ash clouds blotting out the sun, thunderclaps of booming shockwaves and thousands of lightening strikes.
"The clouds that people could see in the distance, the booming noises and then the waves coming from the first tsunami...The next step is when the ash clouds spread across Tongatapu, and that ash cloud is so dense with fine ash particles that it blocks the sun completely, so it gets really dark."
Cronin said rain, small pebbles and many centimetres of ash would have rained down.
"This is an eruption best witnessed from space," he said.
It is possible the Tongan volcanic eruption could lead to a slightly cooler winter and possibly beautiful sunsets in the southern hemisphere this winter.
When a volcano erupts, it releases huge amounts of sulphur dioxide (SO2) into the air, which bounces some of the sun's radiation away.
Climate scientist Jim Salinger has researched the impacts of major volcanic eruptions, including Pinatubo, on the climate in New Zealand.
He said it was not nearly as large eruption as Pinatubo, and would not have a global impact on the climate, but there could be some local effects in the Southern Hemisphere.
Dr Salinger said it could take a few months to kick in and have cooling of about 0.1 to 0.5 degrees, lasting until spring.
"[In] New Zealand it would mean that it might be just a little bit cooler than normal." ■