Annan told reporters that so far, governments have pledged $500 million in aid to disaster victims.
"Let me say that in this particular instance the response has been very good," Annan said in response to a question about the earlier criticisms by U.N. Undersecretary-General for Humanitarian Affairs Jan Egeland on Monday.
The $500 million figure includes $250 million the World Bank pledged Thursday for the victims of the disaster in Southeast Asia, U.N. officials said Thursday.
The announcement was made after Annan met with heads of U.N. agencies and leaders of Non-Governmental Organizations at U.N. headquarters in New York.
"Governments have donated and they have indicated to me that they will do more," Annan said. "I am satisfied with the response so far. The only thing I want to stress is that we are in this for the long term."
He said the disaster is "so huge that not one country or agency can deal with it alone."
Officials said earlier this week that the World Bank likely will redirect money from existing projects in the Asian nations devastated by earthquakes and flooding to provide immediate assistance for reconstruction. On Thursday, the death toll reached more than 114,000.
When Hurricane Mitch damaged several countries in Central America in 1998, the World Bank followed a similar plan to help governments repair transportation, communication and other vital components of their infrastructure damaged by a single natural disaster. At that time, the World Bank organized a $200 million package for immediate relief followed by $1 billion for overall reconstruction.
Agency officials expect to work with the Asian governments to assess their needs, Milverton said.
"It's very tough to work out, at this point in time, what's needed and where," he said. "It really does come down to our guys in each country talking to the governments there to help them work out what is needed straight away."
The World Health Organization said Thursday it needs about $40 million to supply 3-5 million people in the tsunami-struck Indian Ocean region with clean water, shelter, food, sanitation and health care.
Up to five million people lack access to the basic supplies they need to stay alive, the United Nations health agency said.
"This is the most serious natural disaster to affect the region for several decades," said WHO Director-General Lee Jong-wook. "The health needs of the populations affected are immediate and substantial."
"Unless the necessary funds are urgently mobilized and coordinated in the field we could see as many fatalities from diseases as we have seen from the actual disaster itself," said Dr. David Nabarro, head of crisis operations at WHO. "The tsunami was not preventable, but preventing unnecessary deaths and suffering is."
The next few days will be critical in controlling any potential outbreak of waterborne diseases in areas affected by the Indian Ocean tsunamis, Nabarro told The Associated Press.
The incidence of diarrhea is increasing, but is no more than expected at this stage of a natural disaster, Nabarro said.
"We remain really concerned about the situation," he said, adding that the main threat to public health was drinking water that had been contaminated with feces.
"Wells, water supply systems just get broken, and then whatever water you do get is liable to be contaminated," Nabarro said.
Governments are still trying to determine how many were killed in the devastation wreaked by Sunday's quake and the tsunamis it caused. Worst-hit have been Indonesia, Sri Lanka, India, Thailand and the Maldives.
The International Federation of Red Cross and Red Crescent Societies has created a Web site for donations to its aid appeal.
"We are concerned about children under 5 and pneumonia because they are probably quite weak children, they weren't very advantaged children to begin with and so they could be quite vulnerable," spokeswoman Sian Bowen said. "So it is indeed a huge concern."
Sporadic cases of diarrhea are being reported, but the number will "obviously increase" as relief organizations penetrate further into the affected areas, said Jamie McGoldrick, an emergency relief coordinator of the U.N. Office for the Coordination of Humanitarian Affairs in Geneva.
The United Nations is particularly concerned about the situation in Indonesia's Aceh province, which was closest to the epicenter of the earthquake.
"Agencies are now starting to beef up their presence, and I think more importantly for us, we're starting to establish presence in Bandah Aceh, which we think is one of the biggest concerns," McGoldrick said. "We're actively seeking to strengthen that presence."
Nabarro added: "I'm pretty certain the supplies are there, much more it's distributing those supplies to where they're needed, particularly in areas where the infrastructure's so damaged, like Aceh."
The U.N.-affiliated International Organization for Migration said Thursday it is appealing for $10 million to provide help to survivors in Aceh.
"The west coast of Aceh province is 80 percent destroyed, half of Bandah Aceh is in rubble," said IOM's Kristin Dadey. "The needs are colossal."
The group said it has also sent several truckloads of food, water and medicines to affected areas in Sri Lanka.
The World Bank, a specialized agency of the United Nations, includes more than 180 member countries that provide its financing and administration. The agency offers low-interest loans, interest-free credit and grants for projects in developing countries.