Up to a million people are thought to have been left homeless in the crisis, which has left thousands of square kilometres of the Irrawaddy delta under water.
Shari Villarosa, the charge d'affaires of the US embassy in Burma - also known as Myanmar - said food and water were running short in the delta area and called the situation there "increasingly horrendous."
"There is a very real risk of disease outbreaks as long as this continues," Ms Villarosa said, according to Associated Press.
The death toll could reach or exceed 100,000 as humanitarian conditions worsen, she said - based on information from a non-governmental organisation that she would not name.
Before and after: extent of flooding clear in Nasa satellite images
Accounts from the Irrawaddy delta have spoken of fistfights breaking out between survivors desperate to seize dwindling supplies of food and water.
Some are breaking open coconuts for the water inside, while others are driven to eating dead fish.
Poor sanitation, rotting bodies in the water, and flooding could all bring disease, aid agencies warn.
They highlight the risk of mosquito-borne malaria and dengue fever, along with water-borne diseases such as cholera and dysentery.
Calls for access
The Burmese authorities have attracted criticism over claims they are refusing to provide visas to waiting foreign aid workers and have spurned some offers of help, such as a US offer to deploy three naval ships and two planes in the region.
The US Secretary of State Condoleezza Rice is the latest to voice such criticism, telling reporters:
"What remains is for the Burmese government to allow the international community to help its people. It should be a simple matter. It is not a matter of politics."
Earlier, UN Secretary General Ban Ki-moon urged authorities in Burma to assist the entry of foreign aid workers and supplies into the country "in every way possible" - strong diplomatic language, says the BBC's correspondent at the UN, Laura Trevelyan.
Speaking to reporters, the UN's humanitarian chief John Holmes accepted that aid agencies had faced difficulties accessing the disaster zone.
But, he said, co-operation from the Burmese authorities was "reasonable and heading in the right direction".
He dismissed a suggestion by the French Foreign Minister Bernard Kouchner that the UN Security Council should adopt a resolution allowing aid to be flown into the country by force as unnecessarily confrontational.
Mr Holmes said 24 countries had pledged assistance so far worth $30m (£15m), and a flash appeal would be launched on Friday once an initial assessment of need was complete.
An assessment team was due in Burma on Thursday.
A stream of aid is now in, or on its way, to Burma:
The UN says a plane loaded with 25 tonnes of supplies and a small team of rescue staff will arrive in Burma within days
The UN's World Food Programme has dispatched an additional four planes loaded with supplies including high-energy biscuits
Chinese media say a plane carrying 60 tonnes of aid has landed in the biggest city, Rangoon
Planes from Thailand, India and Indonesia are also being dispatched
The WFP has already begun to distribute existing food aid stocks in and around Rangoon, and the Red Cross has a handful of expatriate and many local staff on the ground.
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