So far, she said, the World Food Programme had been able to send only 361 tonnes of food aid - and distribute just 175 tonnes.
Emergency help has been held up by Burma's rulers, who have accepted the aid but refused to allow experts from overseas to co-ordinate its delivery.
Aid agencies say much of the food and equipment arriving in the country is not getting to those who need it because the junta does not have the organisation to transport it.
A BBC correspondent inside Burma says aid delivery is haphazard and private citizens have begun to distribute water and cakes from the backs of their cars rather than waiting for the soldiers to help.
French news agency AFP reported that the military had imposed a curfew in some of the worst-affected areas in the Irrawaddy Delta region over fears that rice rations would be stolen.
"You can't go out after 7pm because the soldiers will shoot," a 60-year-old man from the village of Pyin Ka Yaing told an AFP reporter there.
The BBC's South East Asia correspondent Jonathan Head says much of the aid that has arrived in the country has sat at the airport for days.
He adds that after more heavy rain, the survivors are living in wretched conditions and the fear of a further wave of deaths from disease is a real one.
An aid worker's account of conditions in Burma's Delta region (12 May)
World leaders have stepped up their rhetoric against the Burmese generals in recent days, with UN Secretary General Ban Ki-moon expressing "immense frustration" at what he described as their "unacceptably slow" response.
US President George W Bush described the generals as either "isolated or callous".
"There's no telling how many people have lost their lives as a result of the slow response," he told CBS radio.
Ms Byrs called for "at least an air or sea corridor to channel aid in large quantities as quickly as possible".
The EU's foreign policy chief Javier Solana said the UN must use "all means necessary" to ensure aid got through to those who needed it most.
A US flight carrying about 13 tonnes of supplies including mosquito nets, blankets and water arrived in Rangoon on Monday followed by two flights from aid agencies carrying 56 tonnes of aid.
The UN says it has so far reached 270,000 people - but officials fear more than one million are facing cholera, fever or starvation.
Mr Ban said food aid provided so far might amount to less than a 10th of what was needed, and that rice stocks in the country were "close to exhaustion".
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