The secretive military, which has ruled the former Burma for 46 years and has been shunned by Western governments after a violent crackdown on Buddhist monk-led protests last September, conveyed the message at a meeting with UN officials in Yangon.
The death toll from Saturday's cyclone covered only two of the five declared disaster zones, where UN officials said hundreds of thousands of people were without shelter and drinking water.
"The confirmed number is 3,934 dead, 41 injured and 2,879 missing within the Yangon and Irrawaddy divisions," Myanmar TV reported three days after Cyclone Nargis, a storm with winds of 190 kilometers per hour, hit the Irrawaddy delta.
Government officials gave a "careful green light" to United Nations to send immediate emergency aid, a UN spokesman said.
"The UN will begin preparing assistance now to be delivered and transported to Myanmar as quickly as possible," Paul Risley of the World Food Program said.
The United States, which has imposed sanctions on the junta, said it had provided funds through the World Food Program and other aid groups.
"It doesn't necessarily go directly to the government," White House spokesman Scott Stanzel told reporters. "But we're in the process of assessing what more we can do."
Two Indian naval ships loaded with food, tents, blankets, clothing and medicines would sail for Yangon soon, Indian's Ministry of External Affairs said.
Offers of help have also came from Singapore and neighboring Thailand, while the European Union said it had extra humanitarian staff on standby and was ready to provide aid quickly.
The junta leaders, bunkered in their isolated new capital of Naypyidaw, 400 kilometers north of Yangon, said they would go ahead with a May 10 referendum on a new army-drafted constitution that critics say will entrench the military.
The last major storm to ravage Asia was Cyclone Sidr, which killed 3,300 people in Bangladesh last November.
In the former capital, Yangon, food and fuel prices have soared as aid agencies scrambled to deliver emergency supplies in the five disaster zones, home to 24 million people.
"How many people are affected? We know that it's in the six figures," Richard Horsey, of the UN disaster response office, said after an emergency aid meeting in Bangkok on Monday before the state TV announcement.
"We know that it's several hundred thousand needing shelter and clean drinking water, but how many hundred thousand, we just don't know."
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