The UN says it is extremely disappointed at the slow progress made in securing access to victims of last weekend's cyclone in Burma.
Humanitarian chief John Holmes told reporters that Burma's response was "nothing like as much as is needed".
In addition to about 23,000 people who died in the storm and tidal surge, 1.5 million are at risk, he said.
The US has rejected an idea to air-drop supplies into Burma without permission, after its planes were denied entry.
Some supplies have been allowed into Burma but many more tonnes of aid, and dozens of foreign staff, have not.
In a statement, the UN Secretary General Ban Ki-moon said that Burma's ruling junta planned to press ahead with a constitutional referendum on Saturday, except in the worst-hit areas.
He said it might be "prudent to focus instead on mobilising all available resources and capacity for the emergency response efforts".
Burmese state media say 22,980 people were killed by Cyclone Nargis but there are fears the figure could rise to 100,000.
At his briefing with reporters on Wednesday, Mr Holmes said progress was being made in securing easier access to the many victims, but he is now clearly losing patience, says the BBC's Laura Trevelyan at UN headquarters in New York.
There is a real danger that an even worse tragedy may unfold if we cannot get the aid that's desperately needed in quickly
Mr Holmes warned that the situation was "increasingly desperate".
As many as 1.5 million people were severely affected, he said, and there was a "real danger that an even worse tragedy may unfold if we cannot get the aid that's desperately needed in quickly.
"Frustrations are growing about access," he said.
Four flights carrying supplies from the UN's World Food Programme arrived in Rangoon on Thursday, as well as an International Committee of the Red Cross (ICRC) flight.
But at least 40 UN expert staff are waiting in Bangkok for visas to enter Burma.
Mr Holmes said two out of four members of a specialist UN disaster assessment team had also been denied access when they arrived in Burma, despite apparently having the correct documents.
Secretary General Ban is trying to talk to the Burmese leader, Gen Than Shwe, to persuade him to remove those obstacles.
Reports from Rangoon and the Irrawaddy delta say there is now a greater presence of soldiers carrying out relief work, but that it remains a fraction of what is needed.
Aid stocks are ready to go, but much has not yet been allowed entry
Witnesses in the Irrawaddy delta say sewers and wells are contaminated and stinking, and the corpses of those who died are being left to decompose.
Anger at the slow response to this catastrophe is muted so far, says a BBC correspondent in Rangoon.
But there is potential for that anger to turn political - and it may be for that reason that the military regime here has closed the main Buddhist temples, fearing that they could become the focus for open dissent, our correspondent says.
Earlier reports that the US had been granted permission to fly in military planes loaded with its own supplies have not been borne out - though preparations to use US military equipment in a hoped-for multinational aid operation are continuing.
The US ambassador to the UN, Zalmay Khalilzhad, said he was "outraged" by Burma's slow response to offers of help.
Another US official, Ky Luu, director of the Office of Foreign Disaster Assistance at the US development agency USAid, said one possibility was that supplies could be air-dropped to the afflicted areas without waiting for permission from Burmese authorities.
But when put to Defense Secretary Robert Gates, he rebuffed the suggestion.
"I cannot imagine us going in without the permission of the Myanmar [Burma] government," he told reporters.
The Chairman of the Joint Chiefs of Staff, Adm Mike Mullen, said such a move would violate sovereignty.
Correspondents say it would also risk alienating Burma's regional allies.
France, which has argued that air drops without permission could be allowed under a UN "responsibility to protect" mandate, has once again said it wants to raise the crisis in Burma at the UN Security Council.
But China and Indonesia have countered that the humanitarian problem should not be politicised.
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