The UN says it is optimistic that none of the survivors of the Asian tsunami will lose their lives to hunger.
Aid is being distributed, and no disease has been reported
Jim Morris, head of the UN's World Food Programme (WFP) said he expected food aid to reach almost all survivors within the next seven days.
More than 150,000 people have been killed across Asia. The UN has warned that the toll could rise further as a result of hunger and disease.
But no major outbreaks have been reported so far.
The BBC's Matt Frei says officials in a number of refugee camps in Sri Lanka have told him that disease is being contained and people are recovering.
The WFP head told the BBC that aid had reached "nearly everyone who has been harmed by the disaster".
"Through our partners, a good many NGOs, we've found ways to get food to everyone who's in need," he said.
He said the agency was feeding 750,000 people in Sri Lanka, and up to 150,000 in Indonesia - primarily in Aceh province, the worst-hit by the earthquake and the tsunami on 26 December.
"That number will go above 300,000 in the next few days, probably to 400,000 in the next five or six days," Mr Morris said.
Mr Annan was the latest high-profile visitor to witness the devastation
"Our job is to get food to people to save lives, to address the special nutritional issues relating to women who are pregnant, nursing, and to young children."
Mr Morris said he was optimistic the agency would have everything it needed - an estimated $280m "for food for the next six months, to feed two million people, and for the logistics transport component".
Food distribution to Indonesia, the worst-hit country, is expected to speed up following the opening of a humanitarian air hub at Subang near the Malaysian capital, Kuala Lumpur, on Friday.
It takes almost twice as long to reach the hard-hit province of Aceh from the Indonesian capital, Jakarta, as it does from Subang.