According to CNN, the government confirmed that the death toll was 1,774 on Tuesday; thousands more have been injured, and 660,000 people have been displaced from their homes.
Officials in Tacloban, which bore the brunt of the storm, have said the death toll could be 10,000 in their city. There is grave concern for regions outside Tacloban.
"I think what worries us the most is that there are so many areas where we have no information from, and when we have this silence, it usually means the damage is even worse," said Joseph Curry of the US organisation Catholic Relief Services.
The "sheer size of the emergency" in the wake of the typhoon was testing relief efforts, he told NBC's "Today" program on Monday, speaking from Manila.
John Ging, director of operations at the UN Office for the coordination of humanitarian affairs, said "many places are strewn with dead bodies" that need to be buried quickly to prevent the outbreak of a public health disaster.
"We're sadly expecting the worst as we get more and more access," Ging told reporters at the United Nations in New York. Compounding the misery for survivors, a depression is due to bring rain to the central and southern Philippines on Tuesday, the weather bureau said.
President Benigno Aquino declared a state of national calamity and deployed hundreds of soldiers in Tacloban to quell looting. Tacloban's administration appeared to be in disarray as city and hospital workers focused on saving their own families and securing food.
Nevertheless, relief supplies were getting into the once-vibrant port city of 220,000. Aid trucks from the airport struggled to enter because of the stream of people and vehicles leaving. On motorbikes, trucks or by foot, people clogged the road to the airport, holding scarves to their faces to blot out the stench of bodies.
Hundreds have left on cargo planes to the capital Manila or the second-biggest city of Cebu, with many more sleeping rough overnight at the wrecked terminal building.
Reuters journalists travelled into the city on a government aid truck which was guarded by soldiers with assault rifles. "It's risky," said Jewel Ray Marcia, an army lieutenant. "People are angry. They are going out of their minds."
US, Britain sending warships to help relief efforts
The United States is sending an aircraft carrier to the Philippines to help speed up relief efforts.
The USS George Washington aircraft carrier should arrive in 48 to 72 hours, the Pentagon said, confirming a Reuters report. A statement said crew from the George Washington, which carries some 5,000 sailors and more than 80 aircraft, were being recalled early from shore leave in Hong Kong and the ship was expected to be under way in the coming hours. Other US Navy ships would also head to the Philippines, it said.
The Philippines has been overwhelmed by the scale of Typhoon Haiyan, one of the strongest on record, which tore a path through islands in the central Philippines on Friday.
Rescue workers were trying to reach towns and villages on Tuesday that have been cut off, which could reveal the full extent of the loss of life and devastation from the disaster.
The arrival of the carrier and its aircraft will speed up the distribution of aid and ensure injured survivors can be evacuated to hospitals in unaffected parts of the country.
Britain is also sending a navy warship with equipment to make drinking water from seawater and a military transport aircraft, Prime Minister David Cameron said.
Relief efforts picking up
International relief efforts have begun to pick up, with dozens of countries and organisations pledging tens of millions of dollars in aid.
Operations have been hampered because roads, airports and bridges were destroyed or covered in wreckage by surging waves and winds of up to 235 mph (378 kph).
About 660,000 people were displaced and many have no access to food, water or medicine, the United Nations said. UN aid chief Valerie Amos, who is travelling to the Philippines, released $25 million for aid relief on Monday from the UN Central Emergency Response Fund.
Amos and the Philippines government are due to launch an appeal and action plan on Tuesday to deal with the disaster. Aquino's declaration of a state of national calamity will allow the government to use state funds for relief and to control prices. He said the government had set aside 18.7 billion pesos ($432.97 million) for rehabilitation.
Additional US military forces also arrived in the Philippines on Monday to bolster relief efforts, officials said, with US military cargo planes transporting food, medical supplies and water for victims.
* Terrifying accounts
Rescuers have yet to reach remote parts of the coast, such as Guiuan, a town in eastern Samar province with a population of 40,000 that was largely destroyed.
The typhoon also levelled Basey, a seaside town in Samar province about 10 km (6 miles) across a bay from Tacloban in Leyte province. About 2,000 people were missing in Basey, said the governor of Samar province.
The damage to the coconut- and rice-growing region was expected to amount to more than 3 billion pesos ($69 million), Citi Research said in a report, with "massive losses" for private property.
Residents of Tacloban, 580 km southeast of Manila, told terrifying accounts of being swept away by a wall of water, revealing a city that had been hopelessly unprepared for a storm of Haiyan's power.
Most of the damage and deaths were caused by waves that inundated towns, washed ships ashore and swept away villages in scenes reminiscent of the 2004 Indian Ocean tsunami.
Jean Mae Amande, 22, said she was washed several kilometres from her home by the surge of water. The current ripped her out to sea before pushing her back to shore where she was able to cling to a tree and grab a rope thrown from a boat.
An old man who had been swimming with her died when his neck was gashed by an iron roof, she said.
"It's a miracle that the ship was there," Amande said.