Pakistan's president has appealed for international help, saying his country cannot deal with the aftermath of the massive earthquake on its own.
More than 19,000 people are thought to have been killed in Pakistan, and it is feared the toll could rise much higher.
With some towns and villages completely flattened, Pervez Musharraf told the BBC that Pakistan needed "massive cargo helicopter support" and aid supplies.
The US immediately came forward to offer eight military helicopters.
Many other countries across the world have offered financial help and practical support.
"We certainly look for international help," General Musharraf told the BBC.
"The military has been mobilised completely," he said, but because roads in remote mountainous regions had been blocked or swept away in landslides, there was severe pressure on Pakistan's "limited" transport and helicopter resources.
Pakistani-run Kashmir: At least 17,000 dead
Pakistan's North-West Frontier province: At least 1,600 dead
Islamabad: At least 25 dead
Indian-run Kashmir: At least 600 dead
"Other than that, we of course need relief goods in the form of tents and blankets and medicines," he said.
The earthquake, which hit at 0350 GMT on Saturday, is thought to have been the strongest earthquake in the region in a century.
Pakistani Interior Minister Aftab Sherpao told a press conference the death toll in Pakistan and Pakistani-administered Kashmir had now risen to at least 19,136, and 42,397 had been injured.
Rescuers are struggling to reach remote, mountainous areas, where tens of thousands of people have spent a second night in the cold without shelter.
"It is such a horrendous situation that one cannot imagine. Casualties are increasing by the hour," Mr Sherpao said.
Officials said that 11,000 died in the city of Muzaffarabad, the capital of Pakistan-administered Kashmir.
Many of the victims were schoolchildren, who had just begun classes when school buildings collapsed on top of them.
The city's cricket stadium is being used to house the homeless and offer relief to the survivors. The injured are waiting to be airlifted to hospitals in Islamabad.
Many of the towns and villages in the surrounding areas bore the brunt of the earthquake and have been virtually razed to the ground.
North-West Frontier Province (NWFP) chief minister Akram Durrani said more than 1,800 bodies had been recovered in the region, but he anticipated a final tally of around 8,000 deaths.
"We are in desperate need of assistance. The situation is very, very bad. We need tents, food and everything," he said.
The town of Balakot, about 100km (60 miles) north of Islamabad, was almost totally destroyed.
More than 1,000 bodies have reportedly been dug out of the rubble, including nearly 400 children who were buried alive when their schools collapsed.
There are reports of children still trapped in the rubble. Angry residents say the only outside help so far had been occasional airdrops of food supplies.
Survivors have been trooping along the roads out of the town, many of the people carrying the bodies of dead relatives in makeshift stretchers on their shoulders.
About 200 soldiers are also thought to have been killed in the region by landslides and falling debris.
In the Pakistani capital, Islamabad, rescuers attempted to find survivors in the ruins of the upmarket Margalla Towers residential complex.
A British team of specialists joined Pakistani rescue workers, bringing out alive a man and a woman to cheers and applause on Sunday morning.
Two others were also pulled out alive later in the day, rescue officials told the BBC.
A military spokesman told the BBC that the government's priorities were to evacuate those in need of medical care, establish medical treatment centres on the ground, and provide shelter for thousands of homeless people.
Early relief efforts were hampered by landslides and heavy rain.
Officials in Indian-administered Kashmir said the death toll there was more than 600, with the bodies of 300 people found in one town alone.
Indian ruling Congress Party chief Sonia Gandhi toured the town of Uri, near the Line of Control dividing Pakistani and Indian-controlled Kashmir, and promised government help.
RECENT DEADLY QUAKES
2004 Asian tsunami, triggered by undersea quake - kills at least 200,000
2003 Bam, Iran - kills 26,271
2001 Gujarat, north-west India - kills more than 20,000
1976 Tangshan, China - kills 242,000
1923 Tokyo - kills 140,000
But angry residents in towns nearby said they had received no assistance.
Scores of people gathered on a road out of Uri on Sunday, waving down journalists and soldiers and demanding they go to up to mountain villages, where resident Syad Hassan said 65 people had died.
"All the government people, the press people, they are just driving past," he said.
President Musharraf said he had personally thanked Manmohan Singh, the prime minister of India - a long-time rival with Pakistan for control over Kashmir - for the offer to help with rescue operations.