Myanmar's official media says nearly 32,000 people have been killed and 30,000 are still missing but the UN says the real number may be 102,000 dead and up to a quarter of a million missing.
Two million more people in Myanmar are facing disease and starvation after the May 3 cyclone.
Aid agencies have said that with the military government refusing to grant access to relief specialists, many hundreds of thousands of survivors would be at risk of disease.
Following criticism over Myanmar's guarded approach to offers of outside aid, the military government allowed the first US airlift of emergency supplies.
A military cargo aircraft landed in Myanmar's biggest city of Yangon on Monday carrying water, blankets and mosquito nets.
The airlift from a Thai military base was given the green light after four days of negotiations with the Myanmar government and Lieutenant-Colonel Douglas Powell, the operation's spokesman, said the aircraft was unarmed.
The supplies were transferred to Myanmar army trucks and two more shipments are scheduled to follow.
Al Jazeera's Tony Birtley, who was at the Thai air base, said the flight was not carrying any aid workers and would simply be unloaded at Yangon before heading back to Thailand.
Myanmar's ruling generals - long suspicious of foreign involvement in their country - have been sharply criticised for their handling of the disaster, from failing to provide adequate warnings about the pending storm to responding slowly to offers of help.
Al Jazeera's correspondents on the ground say government restrictions on aid agencies and the scale of the crisis means the little aid that is getting to the country is not getting through to many badly-hit areas.
Ban said he had been in touch with many world leaders to co-ordinate the aid response but had not heard from Myanmar's generals despite phone calls and two letters asking them to let aid workers in.
Some see Ban's news conference on Monday as a response to critics who had said the UN was slow to respond to the crisis in Myanmar.
The secretary-general was on a tour of American cities for most of last week and his humanitarian chief, John Holmes, was out of the country at the start of the crisis.
Holmes said on Monday that the UN's response had not been "stingy" and dismissed questions about whether he should resign.
Possible council action
Three of the UN Security Council's five veto-wielding members - France,
Britain and the US - remain interested in possible action to compel Myanmar's government to open its doors to more aid, diplomats say.
"We'll be pushing the issue in the council," Alejandro Wolff, deputy US ambassador to the UN, told The Associated Press on Monday.
|Western powers are pressing Myanmar |
to let in more help [GALLO/GETTY]
There is no agreement on proposed wording for a statement or resolution, but US officials say their aim is to craft language saying the authorities in Myanmar must do everything possible to accept international help.
However, council diplomats said eight of the 15 members - China, Russia, South Africa, Indonesia, Vietnam, Costa Rica, Libya and Panama - had opposed having the UN body that deals with peace and security take up a humanitarian catastrophe.