The Philippine government says it is facing its biggest ever logistical challenge after Typhoon Haiyan, which affected as many as 11 million people.
Cabinet Secretary Rene Almendras said the government had been overwhelmed by the impact of Haiyan, one of the most powerful storms on record.
The official death toll stands at more than 2,300, but local officials and aid workers say it could rise much higher.
Mr Almendras said the government had responded to the disaster "quite well".
Some residents have expressed anger at the slow speed of the government relief effort.
But the BBC's Jonathan Head in Tacloban, a devastated city of 220,000 on Leyte island, says Wednesday brought the first signs of an organised response.
US military planes have been arriving at Tacloban's ruined airport, delivering World Food Programme supplies, which can be carried by helicopter to outlying regions, and a French-Belgian field hospital has been set up.
Many people have left Tacloban, says our correspondent, but among those left behind there is a growing sense of panic and fear, not just of food running out but of law and order breaking down.
On Tuesday, eight people died when a wall collapsed as thousands of desperate survivors mobbed a food warehouse.
And on Wednesday there were reports of shots being fired in the street and of a teenaged boy being stabbed in the stomach.
With warehouses empty, the main concern for people still in Tacloban was food and water. Some survivors resorted to digging up water pipes for supplies.
On a visit to the city, UN humanitarian chief Valerie Amos said aid was coming in but "the priority has got to be, let's get the food in, let's get the water in".
Health officials warn the worst-affected areas are entering a peak danger period for the spread of infectious diseases.
'Like never before'
Mr Almendras told the BBC he believed the administration was "doing quite well" in handling the crisis, especially as it came weeks after a major earthquake in the same region.
"We have never done anything like this before," he said.
Police spokesman Reuben Sindac denied there was a breakdown in law and order in Tacloban, telling the BBC there was a lot of rumour and misinformation spreading among people who were "in a state of shock".
He said security forces were now in control of key installations, preventing looting and ensuring the safety of aid deliveries.
Typhoon Haiyan - one of the most powerful storms ever recorded on land - hit the coastal Philippine provinces of Leyte and Samar on Friday.
It swept through six central Philippine islands before going on to kill several people in Vietnam and southern China.
Disaster management officials in the Philippines have put the confirmed death toll there at 2,344, with another 3,804 injured as of 20:00 local time (12:00 GMT). They said 79 people were still missing.
However, a congressman in Leyte told the BBC he believed the government was giving conservative estimates of the death toll "so as not to cause undue alarm".
"Just viewing the disaster's scope - its magnitude and the areas affected - we believe that the 10,000 figure is more probable," said Martin Romualdez.
The head of the Philippines Red Cross, Gwendolyn Pang, also said she expected the official death toll to rise.
Christine Atillo-Villero, a doctor from Cebu, managed to board a flight on a military plane to Tacloban, to reach her family home in San Jose, on the outskirts of the city.
"There were dead people lying around. In our backyard we have, I think, six corpses just lying there," she told Newsday on the BBC World Service.
"People are walking around like zombies just looking for food and water.
"My hometown will never be the same again. About 90% of the city is destroyed - nothing left."
The mayor of Tacloban, Alfred Romualdez said a mass grave had been dug on Tuesday. Bodies were still being processed by the authorities on Wednesday but he was hopeful they could be buried soon.
'No climate debate'
The Philippines now puts the number affected at just over 8 million, but the UN Office for the Co-ordination of Humanitarian Affairs (OCHA) says 11.3 million people are in need of vital goods and services, because of factors such as lack of food, healthcare and access to education and livelihoods.
US and British navy vessels have been sent to the Philippines and several nations have pledged millions of dollars in aid.
Speaking to CNN on Tuesday, Philippine President Benigno Aquino warned that storms like Haiyan were becoming more frequent, and there should be "no debate" that climate change was happening.
He said either the world was committed to action on climate change "or let us be prepared to meet disasters".
The World Meteorological Organization (WMO) has said record sea levels this year combined with rising temperatures mean that coastal devastation such as that caused by Haiyan is likely to occur more frequently.
Interim figures released by the WMO show this year is heading towards being among the top ten warmest on record.