With communications severely hampered by an undersea cable being severed, information on the scale of the devastation after Saturday's eruption - causing waves up to 15 metres high - has so far mostly come from reconnaissance aircraft.
But the office of Prime Minister Siaosi Sovaleni said every home on Mango island, where about 50 people live, had been destroyed, only two houses remained on Fonoifua and Namuka island had suffered extensive damage.
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 closest 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 a UK citizen whose death was confirmed on Monday.
A number of injuries were also reported.
The United Nations said on Monday a distress signal was detected in the outlying Ha'apai islands, where Mango is located.
Tsunami waves reaching up to 15 metres had hit the Ha'apia island group and the west coast of Tonga's main island, Tongatapu, the prime minister's office said.
On the western coast of the main island, 56 houses were completely or seriously damaged and residents moved to evacuation centres.
Mango is about 70km from the Hunga Tonga-Hunga Ha'apai volcano, which sent tsunami waves across the Pacific Ocean when it erupted with a blast heard 2300km away in New Zealand.
A search and rescue operation began on Sunday for Atata island, which has a population of about 100 people.
The prime minister's office said some limited communications had been made with satellite phones but some areas remained cut off.
The Tongan navy had deployed with health teams and water, food and tents to the Ha'apai islands, with more aid sent on Tuesday due to the severity of the damage observed on Mango, Fonoifua and Namuka islands, it said.
Water supply had been "seriously affected" by volcanic ash and was a major concern, the prime minister's office said.
Ships carrying supplies and relief equipment, including water, have left from ports in Australia and New Zealand but will take at least five more days to reach Tonga's shores.
Clearing the airport runway of ash is a priority for the government. The archipelago's main Fua'amotu International Airport was not damaged but the ash was having to be manually removed.
The United Nations is preparing for distanced relief operations to avoid a COVID-19 outbreak.
Fiji-based UN co-ordinator Jonathan Veitch said the agency would conduct most operations remotely, and may not send personnel to the island.
"We believe that we will be able to send flights with supplies. We're not sure that we can send flights with personnel and the reason for this is that Tonga has a very strict COVID-free policy," Veitch told a media briefing.
Tonga was one of the few countries that is COVID-19 free and an outbreak there would be disastrous, he said. It has 90 per cent immunisation coverage both in adults and also younger people over the age of 12.
The UN had 23 people on the ground plus other international NGOs to help with relief efforts, Veitch said.
He said the World Health Organisation would start a discussion with the government "in a cautious manner, but we won't be doing anything to threaten the safety of their protocols and the safety of their population in terms of COVID".
