BANGKOK, Thailand — An estimated 1.5 million Burmese are on the brink of a “massive public health catastrophe,” the British charity Oxfam warned yesterday, as desperate survivors of Cyclone Nargis poured out of the devastated Irrawaddy Delta into regional towns in search of water, food, and other help.

Burma is facing a “perfect storm” of conditions that could lead to an outbreak of waterborne disease, Oxfam’s regional director, Sarah Ireland, said.

“The ponds are full of dead bodies, the wells have saline water, and even things like a bucket are in scarce supply,” Ms. Ireland said. She appealed for Myanmar authorities, who have restricted access to the country, to allow humanitarian agencies to send in technical and health experts to help prevent disease outbreaks.

The struggling relief efforts suffered another setback when a boat ferrying rice, drinking water, clothing, and other aid supplies sank in the delta early yesterday, apparently after hitting a submerged tree, the International Federation of Red Cross and Red Crescent Societies said.

Residents were able to salvage some of the supplies, meant for more than 1,000 survivors, but river water probably contaminated the food, the organization said. All of those aboard made it safely to land. The boat was carrying one of the first international aid shipments. “This is a great loss,” the supervisor of the distribution effort, Aung Kyaw Htut, said. “This would have been our very first river shipment, and it will delay aid for a further day.”

The cyclone and powerful tidal sea surge ripped across the low-lying delta a week ago, with winds topping 120 mph. The country’s ruling junta yesterday raised its official tally of the dead to more than 28,000, though humanitarian experts say the toll could run much higher.

Thousands remain missing. The dire warnings came as Myanmar’s state press declared success in a referendum to secure public endorsement of a new constitution that critics say would perpetuate and legitimize military rule. Burma’s leaders say the charter will lay the foundation for a “discipline-flourishing democracy.” With conditions in the delta increasingly desperate, many survivors began besieging small towns, searching for help. In the town of Laputta, which lost 85% of its buildings, about 28 makeshift camps have sprung up.