A United Nations report on the cyclone that struck northern Tonga over the weekend says more than half of the 1130 buildings affected were destroyed and 34% of the rest have major damage.
In its assessment of damage to the severely affected Ha'apai group of islands, the UN Office for the Coordination of Humanitarian Affairs says 13 of the 17 primary and secondary schools affected have major damage.
Cyclone Ian killed one person and made thousands homeless, with more than half of the population of 8000 in the northern island group displaced and food crops wiped out.
The UN report says the most immediate challenge is the logistics of distributing relief to the outer islands.
It says the Tongan government continues to manage the response without a call for formal international assistance, although it is receiving bilateral help from New Zealand, Australia and aid agencies.
Oxfam worker Stuart Kent said there is very little fresh water available on the island group and providing a supply is the highest priority for aid agencies.
Mr Kent says some food needs to be provided immediately and work must then begin on re-establishing devastated crops.