Governments worldwide pledged tens of millions of dollars to help disaster victims, and relief agencies began sending hundreds of tons of food and medicines to the hardest-hit areas.
U.N. Undersecretary Jan Egeland, who is in charge of emergency relief coordination, said the disaster had caused "many billions of dollars" of damage, and could be costliest in history.
The scope of the disaster caused by Sunday's massive earthquake and subsequent tidal waves posed challenges on a scale never seen before, experts said.
Relief organizations used to dealing with one or two crises in the world at a time now have 11 disaster zones, tens of thousands of unburied bodies, millions of people left homeless and the risk of mass outbreaks of disease.
"This is unprecedented," said Yvette Stevens, an emergency relief coordinator of the U.N. Office for the Coordination of Humanitarian Affairs.
The death toll continued rising Tuesday, to about 40,000 people. Sri Lanka, with at least 18,700 dead, was worst hit followed by Indonesia with 15,000. More than 4,300 were dead in India, 1,500 in Thailand and scores each in Malaysia, Myanmar, the Maldives, Somalia, Tanzania, Seychelles and Bangladesh.
In Indonesia, the devastation centered on Aceh province on Sumatra island, the closest land to Sunday's 9.0-magnitude quake that sent deadly waves that swamped coastlines along the rim of the Indian Ocean.
The provincial capital of Banda Aceh was largely destroyed, and communications lines remained cut there and in dozens of other towns on the island, many of which have not been heard from since the quake.
Similar problems were repeated across south Asia.
Indonesia — like governments in some other of the hardest hit countries — has been overwhelmed by the emergency, said Steve Aswin, an emergency officer with UNICEF in Jakarta.
"There is not anyone to bury the bodies," he said. "They should be buried in mass graves but there is no one to dig graves."
Almost all of the nations hit were poor and developing, and will be largely reliant on outside help to cope.
Some nations will be expected to take on more of the burden of relief efforts, said the United Nations, which is coordinating with organizations including the International Red Cross.
"A country like India has a lot of capacity to cope," Stevens said. "In Malaysia, there has been some (impact) but the government can cope."
Meanwhile, relief supplies were starting to trickle into the region's devastated nations.
The U.N. children's aid organization said that about 175 tons of rice arrived in Banda Aceh late Monday and six tons of medical supplies were expected to arrive by Thursday. But most basic supplies were in short supply and there were reports of looting in some parts of the province.
Meanwhile, the Red Cross in Nairobi, Kenya, said in a statement that a plane carrying 105 tons of blankets, medicines and tarps for 50,000 people was headed Tuesday to Sri Lanka.
Earlier the agency — which has launched an appeal for $6.6 million — said it was concerned about the possible spread of waterborne diseases and is sending anti-diarrhea medicine in its aid shipments, said senior health officer Hakan Sandbladh in Geneva.
"We are particularly concerned about initial reports of destruction of hospitals and other health infrastructure in Sri Lanka," Sandbladh said.
The EU announced it would provide $41 million in quake relief and likely more after further assessing the situation.
"There is no doubt we are talking about substantial sums as this is one of the world's worst natural disasters for many years," Louis Michel, the European Commissioner for humanitarian aid, said in a statement.
Japan pledged $30 million and prepared to dispatch its military to help with relief efforts. The United States agreed to provide $15 million has sent a 21-member disaster response team to the region. Australia announced a $7.8 million aid package and sent four C130 Hercules to Indonesia with supplies and a medical team.
The Spanish government said it would provide an airbus to send up to 10 tons of emergency material to Sri Lanka. The U.N. World Food Program has also appealed donations to help meet immediate food needs of victims.