New Zealand's military is sending much-needed drinking water and other supplies, but says the ash on the runway will delay the flight at least a day.
A towering ash cloud since Saturday's eruption had prevented earlier flights. New Zealand is also sending two navy ships to Tonga that will leave on Tuesday and pledged an initial $NZ1 million ($A942,000) towards recovery efforts.
Australia also sent a navy ship from Sydney to Brisbane to prepare for a support mission if needed.
Communications with Tonga have been extremely limited, but New Zealand and Australia sent military surveillance flights to assess the damage on Monday.
"We don't have any further information that would suggest ... significant casualties, although, as you would appreciate, information is still relatively patchy," Australian Pacific Minister Zed Seselja told Nine's Today show on Tuesday.
UN humanitarian officials and Tonga's government "report significant infrastructural damage around Tongatapu", UN spokesman Stephane Dujarric said.
"There has been no contact from the Ha'apai Group of islands, and we are particularly concerned about two small low-lying islands - Mango and Fonoi - following surveillance flights confirming substantial property damage," Dujarric said.
New Zealand's High Commission in Tonga also reported "significant damage" along the western coast of the main island of Tongatapu, including to resorts and along the waterfront area.
Satellite images captured the spectacular eruption, with a plume of ash, steam and gas rising like a giant mushroom above the South Pacific. Tsunami waves of about 80 centimetres crashed into Tonga's shoreline, and crossed the Pacific, causing minor damage from New Zealand to Santa Cruz, California.
The eruption set off a sonic boom that could be heard as far away as Alaska.
Two people drowned in Peru, which also reported an oil spill after waves moved a ship that was transferring oil at a refinery.
New Zealand's Acting High Commissioner for Tonga, Peter Lund, said there were unconfirmed reports of up to three fatalities on Tonga so far.
One death has been confirmed by family: British woman Angela Glover, 50, who was swept away by a wave.
Nick Eleini said his sister's body had been found and that her husband survived. "I understand that this terrible accident came about as they tried to rescue their dogs," Eleini told Sky News.
He said it had been his sister's life dream" to live in the South Pacific and "she loved her life there".
The explosion of the Hunga Tonga Hunga Ha'apai volcano, about 60km north of Nuku'alofa, was the latest in a series of dramatic eruptions. In late 2014 and early 2015, eruptions created a small new island and disrupted air travel to the Pacific archipelago.
Earth imaging company Planet Labs PBC had watched the island after a new vent began erupting in late December. Satellite images showed how drastically the volcano had shaped the area, creating a growing island off Tonga.
The UN World Food Program was exploring how to bring in relief supplies and more staff and had received a request to restore communication lines in Tonga, Dujarric said.
One complicating factor is that Tonga has managed to avoid outbreaks of COVID-19. New Zealand said its military staff were vaccinated and willing to follow Tonga's protocols.
New Zealand's military said it hoped the airfield in Tonga would be opened either on Wednesday or Thursday.
Communications with the island nation is limited because the single underwater fibre-optic cable that connects Tonga to the rest of the world was likely severed in the eruption. The company that owns the cable said repairs could take weeks.
