At the Indonesia aid conference? Mr Annan said there was "a race against time" to prevent another sharp rise in the death toll, now over 150,000.
Global pledges exceed $3bn but promises have not always come good in the past.
The EU is the latest international body to offer increased aid, pledging 100m euros ($132m) to the immediate effort.
Secretary of State Colin Powell said the group – which includes India, Australia and Japan – had served its purpose and would now work with the UN.
Commission President Jose Manuel Barroso said in Jakarta he would also seek the European Parliament’s approval for an additional 350m euros ($464m) for long-term reconstruction.
Meanwhile the US said it was disbanding what it called the core group of nations formed to tackle the crisis.
The BBC’s Laura Trevelyan at the UN says officials who had feared that the core group would duplicate the UN’s efforts will be quietly relieved by this move.
World and local leaders, aid groups and international organisations are attending the Jakarta conference.
Also on the agenda is temporary debt-relief for the Indian Ocean nations affected by 26 December’s disaster and the establishment of a tsunami warning system in the area.
In other developments in the region:
* BBC correspondent Andrew Harding discovers a town in the Indonesian province of Aceh, Teunom, as yet not reached by aid workers
* India builds emergency helicopter pads in the Andaman Islands to speed up aid delivery to remote areas
* UN relief co-ordinator Jan Egeland warns governments and rebel groups in affected areas – specifically in Aceh, Sri Lanka and Somalia – to keep the peace to allow aid work to go ahead
* Saudi Arabia launches a major TV fundraising event for tsunami victims
* The Thai navy starts surveying coastal areas affected by the tsunami with a view to updating shipping charts.
Generosity praised
Mr Annan said the UN had drawn up a "focused set of programmes" tending to the immediate needs of the survivors of the tsunami.
But he warned that the number of fatalities could double if aid did not reach survivors soon.
"There are daunting logistical constraints. But they are not insurmountable. It is a race against time," he told world leaders.
The programmes – costing a total of $977m – would include $215m towards food, $222m toward shelter and $122m towards healthcare.
The biggest single recipient would be Indonesia, the worst-hit country, which would receive $371m of the immediate aid, with the remainder spread across the rest of the region.
Although the UN has praised global generosity in responding to the disaster, aid agencies warn that in past disasters, pledges have not always been honoured.
Just more than a year ago donors promised Iran more than $1bn to assist with the Bam earthquake disaster. Iran complains that only $17.5m ever arrived.
Early warning
Other pledges may come as loans, in services and equipment or be earmarked for long-term reconstruction purposes.
There has been strong support at the meeting for the establishment of an early warning system to alert people to the dangers of any future tsunami.
Mr Annan said prevention and early warning systems must become a priority, and Indonesian officials said a warning system like that in the Pacific Ocean should be set up in the Indian Ocean.
<img src="%%dir[1]%%_40677011_indon_quake_map4_416.gif" border="0" alt="image" name="image" hspace="5" vspace="5" align="left" width="416" height="252" />Also up for discussion will be temporarily relieving the nations affected of their international debt repayments.
Canada remains the only donor to declare a unilateral moratorium on debt repayments, but Japan says it is willing to do so and other countries indicate they would support the idea.
1. Indonesia: 94,081
2. Sri Lanka: 30,513
3. India (inc Andaman and Nicobar Is): 9,682
4. Thailand: 5,288
5. Somalia: 298?
6. Burma: 64
7. Maldives: 82
8. Malaysia: 67
9. Tanzania: 10
10. Seychelles: 1
11. Bangladesh: 2
12. Kenya: 1