"What we urgently need are medical supplies, food, clothes, emergency generators, food and shelter. This flash appeal is timely and welcome."
He added that the first US plane to be allowed in is expected to arrive in Burma on Monday.
Announcing the appeal, UN humanitarian chief John Holmes said it was vital that any obstacles that had hindered aid deliveries until now be resolved soon.
"If we do not act now and do not act fast, more lives will be lost," he said.
Burmese state media say 22,980 people were killed, but the UN fears between 63,000 and 100,000 people could be dead or missing.
A BBC correspondent and aid worker Tim Costello, of World Vision, describe the situation in Burma to Radio 4's The World At One.
The country's ruling generals have faced mounting criticism over their handling of the crisis, their reluctance to allow international aid teams into the country and their insistence on distributing aid themselves.
Mr Ban said he had been unable to contact the head of the ruling junta, General Than Shwe, to ask him directly to allow relief teams in.
"If early action is not taken and relief measures put in place the medium-term effect of this tragedy could be truly catastrophic," he said.
The generals have also been criticised for going ahead with a national referendum on a new constitution on Saturday, while so many people are in desperate need of aid.
The government says the referendum will pave the way for democratic elections in 2010, while the opposition says it is intended to tighten the generals' rule.
The BBC's Andrew Harding says it is a gamble and now there is a chance that public anger could translate into big "No" vote, particularly given the military handling of the storm's aftermath.
The UN fears more than 1.5 million people have been affected by the cyclone, with tens of thousands made homeless and vulnerable to disease.
The World Health Organization says access to clean drinking water and outbreaks of communicable diseases such as dengue and malaria are a major concern.
Hundreds of thousands of people have no food, water or shelter. International aid agencies on the ground say some aid has been distributed in the delta region, but they have reached only 10% of those that need help.
The World Food Programme says discussions with the government will continue about the impounded aid - which includes 38 tonnes of high-energy biscuits, enough to feed 95,000 people.
But regional director Tony Banbury said talks on Friday had stalled and he was worried that a national referendum being held on Saturday would scupper further negotiations.
"I don't know what channels will be open to us to communicate with the relevant authorities, and to encourage them to reverse this very unfortunate decision," he said.
'Murdering own people'
Some charities say they have succeeded in getting some help through but are worried that reports of aid efforts being hampered could stop people making donations if they think it is not making a difference.
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