Meanwhile, the military government proceeded with a vote on a constitutional referendum that it called a "roadmap to democracy," but results may not be known for weeks.
The government said 23,335 people died and 37,019 are missing from the May 3 cyclone, but aid organizations and U.N. officials have said more than 100,000 could die from starvation and disease.
"We are afraid there is a real risk of a massive public catastrophe waiting to happen in Myanmar," British aid group Oxfam's regional chief Sarah Ireland told reporters Sunday.
The Category 3 storm inundated the central low-lying Irrawaddy delta region, destroying villages and wiping out electrical lines. It also slammed the country's largest city, Yangon, in the south.
Survivors are packed into Buddhist temples and schools on the outskirts of the storm's path of destruction.
U.N. staff in Myanmar reported significant progress clearing debris from roadways and restoring the piped water supply in portions of Yangon, according to the Associated Press.
"Aid is getting through in increased amounts," said the International Federation of Red Cross and Red Crescent Societies. The group reported that three of its airplanes carrying 14 tons of shelter materials entered the country without delay.
Two more planes from the U.N. World Food Program, which temporarily halted its shipments Friday after the government refused to let in its workers, also arrived.
But the United Nations said obtaining visas for humanitarian personnel remains a "critical issue," and it continues to work with its regional partners on the matter, reported the AP.
The government has said it will accept international relief shipments, but not foreign aid workers, to instead distribute the supplies on its own.
The United States said it received permission to send a military transport aircraft with shelter supplies, including wood, buckets, nails and plastic tarps, on Monday. The U.S. said it hopes to land two more planes on Tuesday, reported CNN. The supplies will be handed to the military junta.
Besides the slow acceptance of foreign aid, Myanmar's government has been criticized for going ahead with a vote Saturday on a new constitution that it says will pave the way for democracy in the country, though its detractors say it will only solidify the military's rule.
The referendum, which the government said will be followed by general elections in 2010, would guarantee 25 percent of parliamentary seats to the military, and would allow unelected leaders to take control of executive and legislative powers in a state of emergency, reported the Washington Post.
The proposed constitution also would bar Aung San Suu Kyi, whose party won elections in 1990 before the military junta nullified the results, from seeking office.
The vote was delayed by two weeks in areas hardest-hit by the cyclone.