Thousands of children could die within weeks if food does not get to them soon, non-government aid organisation Save the Children said.
The World Food Programme (WFP), leading the outside emergency food effort, said it had managed to get rice and beans to 212,000 of the 750,000 people it thinks are most in need after the May 2 storm, which left at least 134,00 dead or missing.
"It's not enough. There are a very large number of people who are yet to receive any kind of assistance and that's what's keeping our teams working round the clock," WFP spokesman Marcus Prior said in Bangkok.
Save the Children said in a Sunday statement its research had found some "30,000 children under the age of five in the cyclone-affected Irrawaddy Delta were already acutely malnourished before the cyclone hit" on May 2.
"Of those, Save the Children believes that several thousand are at risk of death in the next two to three weeks because of a lack of food."
In the last 50 years, only two Asian cyclones have exceeded Nargis in terms of human cost - a 1970 storm that killed 500,000 people in neighbouring Bangladesh, and another that killed 143,000 in 1991, also in Bangladesh.
With the reclusive military government still refusing to open its doors to a large-scale tsunami-style aid operation, disaster experts say Nargis's body count could still climb dramatically.
To try to offset such a prospect, a steady stream of increasingly important diplomats have been flying into Burma to plead for more access for aid workers and mercy flights.
Pressure is also mounting at the United Nations, where France has accused the junta of being on the verge of a crime against humanity. On Saturday, Prime Minister Gordon Brown condemned the generals' sluggish response as "inhuman".
The French and U.S. navies have ships equipped with aid and helicopters hovering off Myanmar's waters in the Bay of Bengal, but Paris and Washington say they will not start any aid flights from the vessels until they get a green light from the generals.
U.N. chief humanitarian officer John Holmes was due in Yangon on Sunday evening, to meet junta number four Thein Sein, who is prime minister and Burma military aid operations leader.
Holmes was also expected to hand over a third letter from his boss, Secretary-General Ban Ki-moon, to junta supremo Than Shwe, who has refused to talk to Ban on the phone since the cyclone's 120 mph (190 kmh) winds and its 12-foot (3.5 metre) sea-surge slammed into the delta.
