A shell-shocked and thirsty 5-year-old girl was rescued Wednesday, four days after her family's house caved in over her in the devastating earthquake in Pakistan (search) and Kashmir (search).

"I want to drink," Zarabe Shah whispered after rescuers pulled her from the rubble, her cropped hair caked with dust. An elderly man fed her tiny sips of water from a blue plastic bottle cap.

The search teams — who have been using dogs, listening devices and breath-detecting machines in their hunt for survivors — discovered the child and pulled her from the wreckage of her collapsed home, a day after her neighbors found the bodies of her father and two sisters.

"I was scared," said Zarabe, who was buried for almost 100 hours before Russian rescuers pulled her out and took her to a squalid camp where quake survivors are staying with little shelter or food.

The little girl's mother and two other sisters survived Saturday's quake but gave up Zarabe for dead and left Muzaffarabad (search), the capital of the Pakistani portion of the divided Kashmir territory, for a less-damaged city.

A 5.6-magnitude aftershock shook the capital Islamabad early Thursday, causing buildings to move for a few seconds. It was not immediately clear if it caused any damage. The U.S. Geological Survey said the aftershock was centered about 85 miles northeast of Islamabad.

Many bodies were still buried beneath leveled buildings, and the United Nations warned of the threat of measles, cholera (search) and diarrhea outbreaks among the millions of survivors.

Helicopters flying in clear skies delivered aid to victims Wednesday, a day after rain and hail grounded rescue and recovery efforts.

Relief supplies poured into Pakistan from about 30 countries, including 25 tons of tents, medical supplies and food from longtime rival India. The biggest challenge lay in getting supplies to outlying and remote villages.

The Pakistani government's official death toll was about 23,000 people and 47,000 injured, but a senior army official who requested anonymity because he was not authorized to release the figure publicly said an estimated 35,000 to 40,000 people had died.

More than 1,400 people also died in the Indian portion of Kashmir. New Delhi's aid offer and Pakistan's acceptance reflect warming relations between the nuclear-armed rivals who fought two of their three wars over Kashmir and embarked on a peace process last year.

The Indian effort was not without a glitch, however, as a plane from New Delhi was forced to turn around within 10 minutes of takeoff because Pakistan said there was no room to land at the airport. The plane got new clearance for takeoff and arrived in Islamabad before dawn.

Secretary of State Condoleezza Rice (search) arrived in Islamabad on a regional tour and promised long-term U.S. help for Pakistan. She also predicted more American aid beyond the $50 million already committed.

In Washington, Pentagon spokesman Larry Di Rita said 25-30 U.S. military helicopters would be in the region in the next few days. The American choppers ferried about 16 tons of supplies and evacuated more than 100 casualties out of the region on Tuesday, though bad weather forced suspension of some of the efforts, he told FOX News.

U.S. cargo aircraft were also delivering food, water, medicine, blankets, and plastic sheets to the victims.

"We'll provide what we're asked to provide if we have the capability" including mobile hospitals, Di Rita told FOX News, adding that NATO and the United Nations are also involved.

The 7.6-magnitude earthquake demolished whole communities, mostly in the Himalayan region of Kashmir, divided into Indian and Pakistani territories by a cease-fire line near the quake epicenter. The U.N. estimated that 2 million people have been left homeless.

Held close by her uncle, Akmal Shah, little Zarabe described in a soft voice how she fell from the stairs when the quake struck. The stairwell shielded her from the debris above, and she survived without serious injury. She said she was unable to sleep in the dark depths of the rubble, but she did not remember much.

The Russian rescuers who saved her alternated between digging and removing heavy slabs of concrete, requesting complete silence from bystanders so they could get a better fix on the girl's location. One of their tools was a machine that detects carbon dioxide, a sign of breathing.

People can survive under rubble for up to five or even seven days, but dwindling air supply, injuries and dehydration take their toll on those clinging to life.

U.S., Pakistani, German, and Afghan helicopters resumed aid flights suspended because of stormy weather. They brought food, medicine and other supplies to Muzaffarabad, then ferried injured to hospitals. Some 50,000 Pakistani troops joined the relief effort.

Pakistani Prime Minister Shaukat Aziz (search) said small aircraft were able to land at the Muzaffarabad airport, but C-130 transport planes were only able to airdrop equipment and supplies.

Desperate residents mobbed trucks with food and water, grabbing whatever they could. The weak were pushed aside.

Jan Vandemoortele, U.N. resident coordinator for Pakistan, said key roads into the quake zone that were blocked earlier have been opened up. U.S. military spokesman Col. James Yonts said that with the resumption of flights, helicopters were able to release any backlog of aid.

About 30 countries — also including France, Japan, Jordan, China, Russia, Iran, and Syria — and the United Nations have sent relief equipment, doctors, paramedics, tents, blankets, medicines, and disaster relief teams. Many also have pledged financial assistance, and Japan's Defense Ministry said Wednesday it would send about 290 troops and three helicopters to help transport aid.

"Relief material is moving in," Vandemoortele said in Islamabad. "It is getting there. Roads are open now. We have several trucks that are all loaded and on the road now."

The transport plane from India brought tents, medicine and other goods, Foreign Ministry spokeswoman Tasnim Aslam said.

Rescue workers fanned out of Muzaffarabad by helicopter to remote regions of Kashmir — including eight teams from the British International Rescue Corps, which has found 16 survivors since arriving in the quake zone nearly three days ago.

"As time goes on, hope will get less and less. But you always do get miracles," said Ray Gray, a stocky man in a blue uniform and helmet, as he prepared to board a chopper. "Even if we just find one person, the whole effort is worth it."

The quake damaged sanitation systems, destroyed hospitals and left many victims with no access to clean drinking water, making them more vulnerable to disease. The U.N.'s Vandemoortele said there have been no reports of epidemic outbreaks so far but the area's health infrastructure has completely collapsed.

It is too early for onset of disease, but officials are aware of the potential threat, he said. In one field clinic alone, 2,000 patients had been treated, most of them for broken arms or legs.

"Measles could potentially become a serious problem," said Fadela Chaib, a WHO spokeswoman in Geneva. "We fear that if people huddle closely together in temporary shelters and crowded conditions, more measles cases could occur."

Measles — potentially deadly for children — are already endemic in the region and only 60 percent of children are protected. At least 90 percent coverage is needed to prevent an epidemic, WHO said. The agency will soon start gathering essential vaccines for a mass immunization program.

FOX News' David Piper, Bret Baier, Catherine Donaldson-Evans, and The Associated Press contributed to this report.