Meanwhile the junta announced 92.4% of voters had backed their proposed constitution in a national referendum held last weekend.
Human Rights Watch said the result was an "insult to the people of Burma" as there was no way such a majority could have been gained fairly.
The decision to hold a ballot while tens of thousands of people were in dire need of assistance provoked a global outcry against the junta.
The vote was postponed until 24 May in the regions worst-affected by the cyclone.
The proposed constitution entrenches the power of the military, and many observers labelled the referendum a stunt to give a veneer of legitimacy to the junta's reforms.
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Undercover reporter says aid is still in short supply in Burma
In an apparent concession to international pressure, the generals say they will allow 160 foreign aid workers into the country, as well as an emergency relief team from the Association of South East Asian Nations (Asean).
But it was unclear whether the workers - from countries including Thailand, China, India, Bangladesh - would be allowed out of Rangoon into the stricken delta region, where help is most urgently needed.
"Even though the Myanmar [Burma] government has shown some sense of flexibility, at this time it's far, far too short," Mr Ban said.
He told reporters that John Holmes, the UN's top humanitarian official, would accompany the next aid flight into Burma and attempt to negotiate with the junta.
Mr Ban said he "regretted" the UN had spent more time arranging rather than delivering help.
Aid agencies continue to criticise the military regime - accusing the generals of stalling on issuing visas for relief experts, ineptly distributing the supplies they are allowing into the country and blocking access to the worst-affect regions.
A slow trickle of aid is now getting to survivors but the agencies say it is nowhere near enough.
They say far more boats and trucks are needed to get the supplies to the communities that need them most - and far more expert personnel.
The latest Burmese official figures put the number of dead at almost 38,500, with 27,838 more missing, but the Red Cross warned as many as 128,000 could be dead.
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