"We are extremely worried that many children in the affected areas are now suffering from acute malnourishment," said Jasmine Whitbread, chief executive of Save the Children UK.
"When people reach this stage, they can die in a matter of days."
Than Shwe's government has come under growing criticism that it is hampering international relief efforts.
But in a possible signal that the generals are opening up, the UN secretary-general has finally been granted permission to visit the country.
Ban Ki-moon is now due to visit the hardest hit areas of the Irrawaddy delta this week.
The cyclone struck southwest Myanmar, formerly known as Burma, earlier this month and the UN believes nearly 134,000 people have died or are missing, while 2.5 million survivors have been affected.
Thousands of tonnes of aid are being flown in to Myanmar, but relief efforts have been hampered by government restrictions.
|State TV showed Than Shwe visiting survivors |
following allegations he was indifferent
In recent days, Myanmar's rulers have begun to let more foreign experts into the country, more than two weeks after the storm, but aid groups still want greater access to help supervise relief efforts.
Despite the government's insistence that the relief efforts are going well, witnesses who managed to slip the security cordon around the hard-hit Irrawaddy Delta said the situation remains dire.
"It was horrible beyond description," said one foreign businessman.
"Most of the devastated huts looked like they were empty at first glance, but there were actually survivors inside.
"One hut with no roof was full of about 100 people, crouching in the rain. There was no food and no water. Each person had nothing more than the clothes on their bodies, shivering in the cold."
Britain's Asia minister said he thought efforts would soon pay off, with an agreement likely for a UN and Asian-led operation that could solve the impasse.
"I think we're potentially at a turning point, but like all turning points in Burma, the corner will have a few S-bends in it," Mark Malloch-Brown said.
But the minister's optimism follows comments by Gordon Brown, Britain's prime minister, who earlier labelled the military's holding back of aid as "inhuman" and said what had been a natural disaster was becoming "a man-made catastrophe".
John Holmes, the UN's emergency relief co-ordinator, was due to arrive in Myanmar late on Sunday to assess the situation and plead with Myanmar's military leaders for greater co-operation with relief agencies.
A day earlier, officials gave a guided tour of the country's cyclone-hit regions to foreign diplomats and aid workers based in Myanmar.
The diplomats were taken into an area which has been closed off to foreigners, but it was "not good enough to get a clear picture of the damage", according to one diplomat.
"What they showed us looked very good, but they are not showing us the whole picture," Chris Kaye, Myanmar director for the UN's World Food Programme, said.
As pressure mounts on Myanmar's allies to exercise their power, Southeast Asian foreign ministers are due to meet in Singapore on Monday for talks on how to deal with their neighbour.