Officials distributed aid Tuesday from the first international truck convoy to reach cyclone-battered Myanmar, while the UN chief criticized the country's military leaders for their "unacceptably slow response" to the crisis. Even as some 2 million people faced disease and starvation, Myanmar's authoritarian regime continued to bar nearly all foreigners experienced in managing such catastrophes from reaching survivors of Cyclone Nargis. With hundreds of thousands of homes destroyed in the disaster zone, refugees packed into Buddhist monasteries or camped in the open, drinking dirty water contaminated by dead bodies and animal carcasses. Medicine and food were sorely lacking - even as supplies bottled up at the main international airport. The United States, which launched its first aid flight into Myanmar on Monday, planned to rush in more relief supplies on two flights Tuesday. The United Nations said its first aid convoy arrived Monday evening in Yangon overland from Thailand with more than 20 tons of tents and plastic sheets. Andrew Kirkwood of Save the Children said he hopes that Myanmar's government "realizes the scale of the disaster and starts issuing visas immediately and starts facilitating flights and trucks from Thailand and elsewhere." Kirkwood, in a conference call with reporters, lauded Myanmar's private sector for "picking up a lot of the slack" by selling aid groups clothing, materials for shelter and other relief supplies at cost price. Yangon, Myanmar's largest city, was pounded by heavy rain Monday and more downpours were expected throughout the week, further hindering aid deliveries. For many, the rainwater was the only source of clean drinking water. UN Secretary-General Ban Ki-moon chided the junta for its "unacceptably slow response" in helping victims of the disaster and warned of a deepening crisis. "Unless more aid gets into the country - very quickly - we face an outbreak of infectious diseases that could dwarf today's crisis," he said. "I therefore call, in the most strenuous terms, on the government of Myanmar to put its people's lives first." Myanmar's hermetic authoritarian regime made a huge concession Monday by letting the United States - the fiercest critic of its human rights record - bring in relief following prolonged negotiations. The US military C-130 cargo plane filled with 14 tons of water, mosquito nets and blankets was unloaded in Yangon, providing what officials said was help for some 30,000 victims of the May 3 disaster. It was immediately transferred to Myanmar army trucks to be ferried by air force helicopters to the worst-hit Irrawaddy delta, government spokesman Ye Htut told reporters. "We hope they will allow us to do more in the future," said Lt. Col. Douglas Powell, the US Marines spokesman for the operation. "It's really just up to what the Burmese will allow us to do." The official death toll from the cyclone rose by nearly 3,500 Monday to 31,938, with another 30,000 missing; the United Nations and others have said the death toll could reach 100,000 or higher. The first British aid flight packed with plastic sheets to provide shelter to more than 9,000 families was also on its way to Yangon. "The lives of thousands of cyclone survivors are at extreme risk," the World Vision aid group said. "Displaced people are living in appalling conditions in makeshift shelters and camps, where overcrowding and unsanitary conditions are prevalent." Children - many of them orphans - are suffering from fever, diarrhea and respiratory infections, it said. Many survivors complained of getting rotting rice while soldiers kept the best food for themselves. Two planes carrying 56 tons of medical and other aid from Europe-based humanitarian groups also arrived in Yangon on Monday. Three more planes were en route, said Medecins Sans Frontieres, decrying the "growing restrictions" by the military on the movement of aid within the country. Britain's opposition Conservative Party leader David Cameron, meanwhile, called for airdropping aid into Myanmar even without the junta's approval. "The sands of time are running out," he told BBC Radio. "In the end, what matters is getting aid through to people and feeding them and stopping them from dying." US Defense Secretary Robert Gates said last week he could not imagine dropping aid without the consent of authorities and British Prime Minister Gordon Brown seemed to agree. However, French Foreign Minister Bernard Kouchner said airdrops could be allowed under the UN's "responsibility to protect" mandate.