YANGON, Myanmar (CBS/AP) The Red Cross estimated that the cyclone death toll in Myanmar could be as high as 128,000 - a much higher figure than the government tally. The U.N. warned a second wave of deaths will follow unless the military regime lets in more aid quickly.
The grim forecast Wednesday came as heavy rains drenched the devastated Irrawaddy River delta, disrupting aid operations already struggling to reach up to 2.5 million people in urgent need of food, water and shelter.
Henrietta Fore, an administrator with the State Department's USAID agency, told CBS News Wednesday that "somewhere between 1 million and 2 million people" had been displaced in Myanmar.
"Another couple of days exposed to those conditions can only lead to worsening health conditions and compound the stress people are living in," said Shantha Bloemen, a spokeswoman for UNICEF.
A tropical depression in the Bay of Bengal added new worries, but late in the day forecasters said it was weakening and unlikely to grow into a cyclone.
Myanmar's government issued a revised casualty toll Wednesday night, saying 38,491 were known dead and 27,838 were missing.
The International Federation of Red Cross and Red Crescent Societies, however, said its estimate put the number of dead between 68,833 and 127,990. The Geneva-based body said the range came from a compilation based on other estimates from 22 different organizations, including the Myanmar Red Cross Society, and on media reports.
Even though the figures seemed precise, spokesman Matthew Cochrane said they were not based on body counts, but were only rough estimates designed to provide Red Cross donors and partner organizations with an idea of the numbers being discussed within the aid community.
U.N. officials have said there could be more than 100,000 dead.
The Red Cross estimated the number of people needing help after cyclone surged over the low-lying delta on May 3 at between 1.64 million and 2.51 million.
But the junta still refused to accept help from foreign aid experts, who have vast experience in handling humanitarian crises.
It insisted Myanmar can handle the disaster on its own - a stance that appeared to stem not from the isolationist regime's ability but from its deep suspicion of most foreigners, who have frequently criticized its human rights abuses and crackdowns on democracy activists.
Meanwhile, Myanmar announced Thursday that a new military-backed constitution was overwhelmingly approved by voters in last week's referendum.
State radio said the draft constitution, which critics say is designed to solidify the military's rule, was approved by over 92 per cent of the 22 million eligible voters. It put turnout at more than 99 per cent.
Voting has been postponed in two regions battered by the deadly cyclone but the results of the late balloting cannot mathematically affect the outcome.
The document guarantees 25 per cent of parliamentary seats to the military and allows the president to hand over all power to the armed forces in a state of emergency.
Critics say these elements contradict the junta's professed commitment to democracy.
"The government has a responsibility to assist their people in the event of a natural disaster," said Amanda Pitt of the U.N. Office for Humanitarian Affairs.
"We are here to do what we can and facilitate their efforts and scale up their response. It is clearly inadequate, and we do not want to see a second wave of deaths as a result of that not being scaled up," she said.
Myanmar's prime minister, Lt. Gen. Thein Sein, told visiting Thai Prime Minister Samak Sundaravej on Wednesday that the government was in control of the situation and didn't need foreign experts.
Samak said after returning to Bangkok that the junta gave him a "guarantee" that there was no starvation or disease outbreaks among survivors.
But critics say the government is woefully lacking in helicopters, trucks and boats as well as planning expertise needed to distribute aid to survivors, who have jammed into monasteries and relief centers or are camping outside.
U.N. agencies and other voluntary groups have been able to reach only 270,000 of the affected people, said Elisabeth Byrs of the U.N. Office for Humanitarian Affairs in Geneva.
She said the World Food Program would need 55,000 tons of rice to feed 750,000 people for three months, but the agency had been able to ship in only 361 tons so far.
The junta did grant approval Wednesday for a Thai medical team to visit the delta, said Dr. Thawat Sutharacha of Thailand's Public Health Ministry. If the team goes as scheduled Friday, it will be the first foreign aid group to work in the ravaged delta.
Myanmar has limited the few international aid workers in the country to Yangon, the country's biggest city, and used police to keep foreigners from going to the delta.
The government gave a little ground to demands that it let in more experts. It announced it would allow in 160 relief workers from neighboring countries - India, China, Bangladesh and Thailand. It was not clear whether they would be permitted to go to the delta.
In New York, U.N. humanitarian chief John Holmes welcomed the junta's move. But he said it was not enough and demanded that Myanmar open its borders to foreign relief specialists and let outsiders work in the Irrawaddy delta.
© MMVIII, CBS Interactive Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.