All of the homes on one of Tonga’s small outer islands have been destroyed, it also said.
The office of prime minister Siaosi Sovaleni said that every home on Mango island, where around 50 people live, had been destroyed, while only two houses remained on Fonoifua, and Namuka island had suffered extensive damage.
It comes amid fears of a possible humanitarian crisis developing, but information about the extent of the damage has been scarce as the tsunami severed an undersea cable, cutting communication from the rest of the world.
Tonga’s deputy head of mission in Australia, Curtis Tu’ihalangingie, earlier said pictures taken by the New Zealand Defence Force showed “alarming” scenes of a village destroyed on Mango and buildings missing on Atata island, which is closer to the volcano.
“People panic, people run and get injuries. Possibly there will be more deaths and we just pray that is not the case,” Tu’ihalangingie told Reuters.
Sovaleni’s office said a 65-year-old woman on Mango Island and a 49-year-old man on Nomuka Island had been killed, in addition to the British animal charity worker Angela Glover whose body was found on Monday.
A number of injuries were also reported.
Tsunami waves reaching up to 15 metres hit the Ha’apia island group, where Mango is located, and the west coast of Tonga’s main island, Tongatapu, the prime minister’s office said.
Residents were being moved to evacuation centres as 56 houses were destroyed or seriously damaged on that coast.
Meanwhile, New Zealand is delivering aid to the stricken island group, but ash on the capital Nuku’alofa’s main airport runway is stopping relief planes from landing.
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It will also take days before military ships with supplies will reach the cluster of 170 Polynesian islands, New Zealand authorities said.
New Zealand and Australia have conducted surveillance flights to assess the damage.
On Tuesday New Zealand foreign affairs minister Nanaia Mahuta said “water is among the highest priorities for Tonga at this stage”.
Aid agencies predict volcanic dust and the subsequent tsunami have contaminated Tonga’s water supplies.
She said a C-130 Hercules aircraft was on standby to fly to Tonga’s capital Nuku’alofa to deliver humanitarian aid including collapsible water containers, generators and hygiene kits.
“However images show ashfall on the Nuku’alofa airport runway that must be cleared before (the plane) can land,” she said.
On Monday about 200 Tongans had started sweeping the runway, successfully clearing a 100m (330ft) stretch of tarmac, but there remained “a long way to go”, according to TVNZ reporter Barbara Dreaver.
Ms Mahuta also said two navy ships carrying water supplies, disaster relief stores, and a rescue helicopter will be dispatched to Tonga. However the ships are expected to take three days to arrive.
New Zealand’s Acting High Commissioner to Tonga, Peter Lund, said the local government had declared a state of emergency and that the extent of the destruction was starting to come to light.
“[There is] damage to buildings, there’s a lot of rubble and rocks that have been thrown up but people are now trying to get back to normal in the capital,” he told 1News, adding that clean-up efforts were under way to get rid of the “thick film of ash” blanketing the area.
Mr Lund also said three deaths have been reported, but that these were unconfirmed. It is also unclear whether the number includes the confirmed death of 50-year-old British national Angela Glover, who died as she was washed away while trying to save her dogs.