More than 150,000 people are believed to have lost their lives in the Indian Ocean tsunami last week, and the exact figure may never be known, the UN says.
More than 1.7m people will have to be fed for months, says the UN
"I'm sure it will be higher than that," said relief co-ordinator Jan Egeland.
As ships and aircraft with aid arrived in the afflicted areas, Mr Egeland praised the "international compassion".
He said $2bn had been pledged so far - more than all the pledges for the whole world in 2004. Japan became the single largest donor on Saturday with $500m.
United Nations Secretary General Kofi Annan will travel to the worst-affected country, Indonesia, on Thursday to attend a meeting of world leaders to discuss further aid.
At least 124,000 people have been confirmed dead across the region.
Thousands are still missing after a huge undersea earthquake struck off the Indonesian island of Sumatra on Sunday, sending giant waves smashing into coastlines from Malaysia to East Africa.
Other tsunami developments:
- Survivors in the Indian Andaman and Nicobar Islands - where foreign aid organisations have largely been refused access - complain that authorities have done little to help
Reports emerge of more than 1,000 children dying in a remote school in the Indian state of Tamil Nadu where they tried to take refuge during the disaster
- Thai Prime Minister Thaksin Shinawatra says an investigation will be held to find out why there was no early warning of the disaster
- Sweden, the Western country thought to be worst hit by the disaster, is holding a day of mourning, along with Norway and Finland.
'Never like this'
Mr Egeland told reporters in New York a final definitive casualty figure would never emerge - the world will "never ever know how many people were washed to sea and will never ever be found".
More than 40 countries have pledged support, Mr Egeland said and praised donors' generosity.
"The international compassion has never been like this," he said.
Mr Egeland said the aid effort would focus on feeding one million Indonesians and 700,000 Sri Lankans for months to come.
He said the biggest constraints were logistical - helicopters, helicopter carriers, boats and hundreds of trucks were needed to bring food, water, medicine and other basics to survivors.
"Military assets are as valuable as cash or gold because it make us get there in the race against the clock," he said.
A US aircraft carrier arrived in Indonesia on Saturday, sending helicopters to Indonesia's worst-hit province of Aceh. Transport planes headed for Sri Lanka and Thailand.
American, Australian and Singaporean military personnel are on hand to assist their Indonesian counterparts.
More helicopters are needed to reach remote areas
The US has also supplied 80 trucks to distribute aid.
But Indonesian officials said distribution networks were still not in place to get aid into remote areas - the province's ravaged infrastructure being a major obstacle.
And scenes at Banda Aceh's tiny airport were chaotic on Saturday, owing to a shortage of manpower and storage space, says the BBC's Rachel Harvey in Aceh.
Until now there has been little sign of a co-ordinated relief operation for the estimated two million people who have been displaced in Aceh.