With only half the cash so far pledged to the UN actually paid out, relief coordinators say more international appeals will be inevitable.
Bush Thursday signalled plans to increase US contributions to wave-stricken nations to 950 million dollars from 350 million dollars.
If Congress approves the package it will more than match the 859 million dollars already pledged by 53 donor nations and make the United States by far the largest donor.
Another 57 million dollars has been pledged to UN programmes like the childrens' fund UNICEF and the refugee agency UNHCR by private donors.
However, the United Nations Development Programme (UNDP) overseeing long-term reconstruction efforts says that will not be enough to rebuild the Indian Ocean coastal communities shattered by the December 26 tragedy.
"Once these countries have got through the relief phase we have a long, long way to go before people are moved out of tents and into homes and before towns, jobs and lives are rebuilt," UNDP spokeswoman Cherie Hart told AFP. "There is much more work ahead."
Almost 300,000 people were killed in the tsunamis sparked by a massive undersea earthquake off the coast of Indonesia.
The war-ravaged Indonesian province of Aceh was worst hit, with 231,300 listed as dead. Sri Lanka, India, Thailand and the Maldives also suffered heavy casualties.
The crushing waves destroyed thousands of homes and businesses, shattering the lives of hundreds of thousands of survivors.
UN Secretary General Kofi Annan issued a "flash" appeal for 977 million dollars in immediate aid in the wake of the tsunami.
So far less than half the amount pledged -- 423 million dollars -- has actually been paid out or disbursed among UN agencies, Hart said.
Among the biggest donors were Germany, which has promised 668 million dollars, not including loans, and Australia, which announced its biggest aid package ever of 762 million dollars including loans.
Japan said it has already paid the 500 million dollars cash it pledged.
However, Annan's appeal was for money to see the relief effort through to June, after which more appeals will be launched.
"We're not sure if we will have one big donor conference or a series of conferences in affected countries after June, but a longer-term donor appeal will be necessary," Hart said.
The money pledged to the United Nations does not include donations to non-governmental relief agencies, which have managed to collect considerably more.
When those contributions are factored in, UN relief officials estimate that some 5.4 billion dollars have been pledged in total.
That figure includes a record 1.167 billion dollars collected by the Red Cross and Red Crescent societies; enough, its secretariat says, to fund relief and reconstruction efforts into the next decade.
According to its website, by the end of last month the relief agency had sent 18 emergency response units and 77 relief flights to help more than 500,000 people.
That provided 115,000 people with clean water and 1,000 people with basic medical care every day, it said, adding that the money has also provided shelter to 40,000 people as well as counseling to 11,000.
Relief agency Oxfam said it has raised 200 million dollars while Medecins Sans Frontiers (Doctors Without Borders) said it has raised 117 million dollars.
Separately, the Asian Development Bank said it will hold a high-level ministerial meeting in Manila next month to coordinate how best to use 775 million dollars it has set aside to help tsunami-ravaged countries.
With money now being directed towards reconstruction programmes after a successful emergency response, Hart said the relief effort is now entering a critical phase.
"We are in that gap between relief and reconstruction when we have to start turning our attention to getting these people's lives and businesses back on track -- we have to start planning for the long-term."