Cradled in her mother’s arms inside a tent on the edge of the field is Pakistan’s youngest refugee. Aman, a baby girl, was born just days after her parents fled last month’s fighting in the Buner Valley.

As the Pakistani military moved in to push back against Taliban fighters edging closer to the capital, the family traveled in the opposite direction, across the mountains that form a backdrop to the camp in which they now live.

They are among an estimated 2.4 million Pakistanis who have been displaced, marking a refugee crisis on a scale comparable to the mass flight from Rwanda in the 1990s.

"It took us more than 24 hours to get here,” says Roedad Khan, Aman’s father. "Half of that time, we walked on foot.”

Last month, after the Taliban rampaged through Khan’s village of Kalpani, his neighbors formed a militia to resist the encroachment.

But the insurgents’ advance was only halted by the arrival of gunship helicopters, artillery brigades and fighter jets. As the military’s thunderous assault grew closer, Khan and his wife fled, hiding for hours in the nearby forest.

When daylight broke, they scaled the hills and made their way to Shewa Adda, a village near the town of Swabi. "My daughter was born four days after we arrived,” says Khan.

The camp, now home to 500 families like the Khans, has been named after her: Aman, the Urdu word for peace.

The Khans’ choice of destination was relatively fortunate. Khan and 15,000 others are the guests of the Tarakai family. On land that they own, and inside the schools they built, the wealthy political clan has established an impressive relief operation that boasts ambulances, clinics, visiting doctors, a constant supply of electricity and food, and a small army of volunteers.

But they are the exception. An overwhelming majority of Pakistan’s newly displaced are living in private homes in towns across the northwest, where they are provided with shelter but are struggling to find food or medical attention.

While international aid agencies focus on the camps, the hundreds of thousands of refugees staying outside them are unregistered and, as a result, cannot access crucial supplies.

Stepping into the vacuum created by the government’s faltering response to the crisis was a natural step for the Tarakai family, says Liaqat Tarakai, the acting head of the family.

"We have been doing charity work for a long time,” he says.

Every night during the Muslim month of Ramadan, the vast kitchens located on the edge of the sprawling Tarakai estate feed some 50,000 people from this region.

When the recent military offensive began, the Tarakais’ operation started to cook food and take it to the people from Buner staying with communities in Swabi that were hosting the refugees.

"When those areas became full,” says Tarakai, "we set up our own camps. Today we are setting up the 11th camp.”

Each day brings new arrivals to the camps dotted among the vast stretches of land belonging to the family, where the family grows sugar cane, wheat, corn and very lucrative quantities of tobacco.

The family also operates power projects, and recently acquired the Pakistan franchise for Gloria Jean’s, the café chain. They own a tire factory in Swat’s main town of Mingora, but, like much else in the valley, it was seized by the Taliban.

In recent years, Liaqat Tarakai has slowly pushed the family into the political arena as well. "We have no need of government help,” he proudly declares.

"We are self-sufficient.” Yet even here, refugees are facing difficulties seen elsewhere in the northwest. Though the camp tents are well protected against heat and even have fans inside, daytime temperatures nudge past the 100-degree mark.

The people of Buner and Swat — who are more accustomed to the cool mountain air — are suffering from dehydration, skin rashes, diarrhea and the mounting threat of disease.

Dust has caused respiratory infections and there are widespread psychiatric problems, doctors visiting the camps report. Aman’s mother was one of 66,000 pregnant woman estimated by the U.N. to be among the displaced.

A few tragically lost their babies while fleeing the war zone; most have no access to obstetricians. The crisis could get worse if crucial steps are not taken now.

Despite what has become a public outpouring of support for the refugees with civil-society groups, aid agencies and the local media leading a high-profile campaign to marshal resources, funds are running perilously low.

Last Friday, the UNHCR raised the dollar figure required to over $500 million. Of that amount, only $88 million is in its sights.

The remainder, the UNHCR says, is needed urgently to "to help the most vulnerable and worst-affected people through the end of 2009.”

For its part, Washington has already pledged $110 million — the vast bulk of it going directly to the U.N. and a slew of international aid agencies operating in the area. Still, Prime Minister Yousaf Raza Gilani has asked for more support.

The need for the international community to step up its aid effort was underscored a fortnight ago by the reemergence of Jamaat-ud-Dawa, a banned charity linked to last November’s Mumbai massacre, at the center of relief efforts in Mardan.

Fears have also been growing over the fate of up to 20,000 civilians trapped in Mingora, Swat’s main town, as the army and the Taliban continue to battle each other street by street.

In recent days, the army has claimed a flurry of successes: recapturing key intersections in Mingora, retaking Pakistan’s only ski resort at Malam Jabba that was being used by the Taliban as a training camp and logistics base and clearing the former militant stronghold of Matta.

Militants are now reportedly retreating from Mingora to Kabal. The army has made a push toward Kabal, but it says it is facing "stiff resistance” there.

At a girls’ school built by the Tarakais, recently arrived refugees from Swat describe the Taliban’s preparations for the military offensive. (Schools across the North-West Frontier Province have closed for six months and their buildings are being used to house refugees.)

"The Taliban took over the food shops and changed the locks,” says Mohammad Ali, 30, who used to sell clothes in Mingora’s main bazaar.

"They occupied a high school to make their base there. In the town there was a stock of wheat flour that had arrived for us from the government of Punjab. The Taliban took that over also. They stole government vehicles for their own use.”

Back at Aman camp, Liaqat Tarakai inspects a building that once served as a storage facility for his tobacco.

"I am going to make this into a hospital,” he says.

"We will have a ward, equipment, everything.”

But even he realizes that there are limits on how much he can do, and for how long. The army claims to have cleared much of Buner and has begun to call residents back.

In the coming weeks, Aman’s parents may be able to take their baby home. "But the Swatis will be staying,” says Tarakai, "for some time.”

TIME