As authorities in this typhoon-
ravaged nation struggled Tuesday with a mammoth relief effort, survivors were becoming increasingly desperate, short on food and supplies and terrified about waiting longer for help.

A few residents of hard-hit areas scrawled signs with a simple message: “Help us.”

About five days after the once-
in-a-century winds
of Typhoon Haiyan gashed the central Philippines, some aid workers said progress has been too slow. Many who want to help are waiting at airports and air bases, hoping to catch rides from the short-handed Philippine military.

The typhoon directly affected about 10 percent of the population, officials have said.

The government’s official death tally rose to 2,344 on Wednesday, the Associated Press reported, citing the National Disaster Risk Reduction and Management Council. President Benigno Aquino III told CNN that the death toll could be 2,000 or 2,500, the wire service said, considerably lower than earlier estimates by two officials on the ground that as many as 10,000 may have been killed.

At least two Americans were among the confirmed dead, according to the State Department.

[See the latest photos from the Philippines.]

Although more than 30 countries have pledged aid, daunting problems have held up the distribution of goods. Some roads are impassable, and many towns have lost their emergency workers.

On Tuesday, some commercial flights to the devastated region were canceled as a much milder tropical storm dumped more rain.

[Read: U.S. groups send relief.]

In Cebu province, the government is using Mactan Air Base — a former U.S. Air Force facility — as a staging ground for emergency work. But Tuesday, only two of the three C-130 military transport planes based at the site were operational; the third was awaiting repairs.

Hundreds of people huddled in a dark waiting room on the base, hoping to board a plane carrying relief supplies.

A badly-damaged hospital in typhoon-hit Tacloban City is overwhelmed with casualties, as a U.S. navy ship with aid and troops heads for the Philippines. (REUTERS)

People with relatives in disaster areas had camped out there for hours, even days, holding plastic bags containing supplies — packaged noodles, bottled water, biscuits. Sitting alongside them on hard plastic chairs were aid workers, eager to assess the needs on the ground and mobilize assistance.

“You see how difficult [it is] getting access to the C-130s,” said Jorge Durand Zurdo of the Spanish Red Cross, part of a five-person team that hopes to get to Tacloban, a city where 10,000 are feared dead.

Zurdo said his group can set up mobile water-treatment plants to address a severe shortage of potable water. “We can treat dirty and muddy waters, rainwater, polluted wells, rivers and streams,” he said.

Marine Brig. Gen. Paul Kennedy, who is leading the U.S. relief mission in the Philippines, said efforts have been hampered because the disaster-hit area has only one adequate airstrip — in Tacloban. And it can handle only lighter aircraft. The runway is overrun with piles of relief supplies. For now, planes have been allowed to run only during daylight because of a power outage.

But as of Wednesday, Kennedy said, flights are expected to run through Tacloban 24 hours a day. Emergency crews are working to install beacons and lighting that will allow for night takeoffs and landings.

In the first hours after Haiyan barreled through, the Philippine government had said, cautiously, that the country might have escaped major damage. Then details of the devastation trickled in from remote areas.

Photographs taken from helicopters showed entire towns — what had been a patchwork of colorful roofs and palm trees — churned and flattened into a brown, wet rot.

Tuesday brought a sharper sense of the battle for survival, as journalists and those involved in the rescue effort reached harder-hit areas.

Medellin, a town in northern Cebu, has run out of syringes and tetanus vaccines, Philippine news organizations reported. In another town, Tabogon, hungry and thirsty children took to the streets with placards saying they needed help, a Philippine journalist said on Twitter. Photos showed survivors using any available materials for shelter. One man rested under sheet metal held several feet above the ground by furniture.

The typhoon also has harmed many local government officials who would ordinarily be an integral part of the relief effort. The Department of Public Works and Highways is trying to reopen roads with the help of local workers, who may have lost homes and family members, said Rogelio Singson, the head of the department. There were widespread outages of electricity and cellphone service.

In Basey, a town that has lost at least 429 of its 50,000 people, buildings were so severely damaged that the local disaster-
management council was rendered “helpless,” Christine Caidic, a provincial official, said in an interview with the Philippine television station ABS-CBN.

National relief operations have been slow to start, partly because local governments weren’t able to quickly report the extent of their needs.

“What we’ve learned this time is that we have to evacuate the social workers first,” before the arrival of any major storm, so that they can assist the victims later, said Mar Roxas, secretary of the Department of Interior and Local Government.

[Read: Why the Philippines wasn’t ready.]

The Department of Social Welfare and Development’s regional office in the city of Cebu says it is trying to assemble 50,000 family-meal packs per day — rations of rice and canned goods. But it has distributed only 25,000 such packs. The office says that about 4 million people were affected in the region.

Edna Gesulgon, a 49-year-old teacher whose family in Tacloban survived the storm, was waiting at the Mactan Air Base, hoping to board a flight so that she could help her loved ones. She said she had heard from relatives about decomposing bodies lying in the open, the stench filling the air.

“I’m appealing to all the people of the world to donate food,” Gesulgon said. “The people now are so devastated, angry.”

The aftermath of Haiyan is proving to be the largest crisis in memory for this disaster-prone country, with more than 600,000 people displaced. Festering bodies and a lack of clean water increasingly pose the risk of disease.

President Obama spoke Tuesday to President Benigno Aquino III, emphasizing “the need for a speedy assessment of what further American resources would be most helpful” in the recovery effort, the White House said. Washington has dispatched Navy ships and disaster-assistance teams; it also has committed $20 million in humanitarian aid.

Britain is sending a navy destroyer with forklift trucks, water-purification kits and emergency supplies, according to a British government Web site.

The United Nations’ humanitarian chief, Valerie Amos, arrived in the Philippines on Tuesday and appealed for $300 million in international assistance.

“I am concerned that there are thousands of people who need help that we have not been able to reach,” she said. “The scale of the destruction is shocking.”

Aquino has sent in police and the military to improve security. Some local police crews are barely functional. In Tacloban, only 20 of the city’s 293 police officers have shown up for duty, Roxas, the interior secretary, told the Reuters news agency.

A woman waiting for a seat on a plane at Mactan, Cynthia Kempis, 33, said she was in Tacloban with her sister when the storm hit. She managed to get to Cebu, but her sister stayed in Tacloban to fend off looters. Kempis was trying to return there with food.

“We had to rush to the kitchen and hide under the sink. Then, suddenly, we felt the water rising from the floor,” Kempis said in an interview. “And soon, it was knee-level, so we had to get up, grab the two children and get on top of the sink.”

Because Kempis cannot swim, she, her sister and the children, ages 5 and 8, clung to a plastic-and-foam sofa and floated for several hours inside the flooded house.

“Soon, our heads were pressed against the ceiling,” she recalled. “I said, ‘We need to get air.’ We floated to the next room, whose roof the storm had blown away.”

Harlan reported from Manila.