Only a quarter of the 2.5m affected have received help, the UN says
Aid agencies have cautiously welcomed Burma's decision to let all foreign relief workers into cyclone-hit areas.
The UN World Food Programme said the real test was whether staff had access to the badly-hit Irrawaddy Delta.
In Thailand UN Secretary General Ban Ki-moon opened a new base to speed up aid for victims of the cyclone, which killed 78,000 and left 56,000 missing.
Meanwhile polls closed in the final stage of a controversial Burmese referendum on a new constitution.
The vote took place in Rangoon and parts of the Irrawaddy delta.
Analysts say the few million voting here will not have been nearly enough to overturn a massive majority in favour of the new constitution, which the Burmese leadership claimed during the main stage of the vote earlier this month.
Mr Ban, who returns to Burma on Sunday for an international donors' conference, described the new base in Thailand as a critical staging area for the relief effort for Cyclone Nargis, which hit on 2 May.
"It will enable larger planes to be used, more aid to be flown in from all over the world, it will save lives," he said.
The BBC's Chris Hogg in Bangkok says some aid has already accumulated in a cavernous warehouse in the city's old airport, which will be sorted so that the most urgent shipments can be prepared for loading.
The UN has chartered three cargo planes to carry it into Burma.
Thousands of aid workers are also needed for the relief effort, and the massive reconstruction that must follow.
For weeks, Burma's government - suspicious of foreigners and fearful of any development which could challenge its monopoly on power - has blocked foreign aid workers.
The change in the Burmese generals' hardline position on access came after a meeting on Friday between Mr Ban and Burma's senior general, Than Shwe.
After talks in Burma's remote capital, Nay Pyi Daw, Mr Ban said Burma would now allow the delivery of aid "via civilian ships and small boats".
But his wording suggested that the US, British and French warships waiting off the coast with supplies may not be able to dock.
Correspondents say Burma has a record of withdrawing promises made to the UN, and aid agencies are waiting to hear how these new arrangements will work in practice.
Burmese monks on a secret trip to hand out aid
The World Food Programme says it has now been allowed to bring in 10 helicopters to ferry supplies to the disaster zone.
The international organisation Medecins Sans Frontieres says it now has some foreign staff working in four areas of the Irrawaddy Delta.
There is also a Thai medical team working there.
The UN estimates that only a quarter of the 2.5 million Burmese affected by the cyclone have received the help they need.
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