Rescuers struggled to reach victims of the devastating earthquake that struck near the Indian-Pakistani border in the disputed Kashmir region Saturday. The quake killed thousands of people, most in remote parts of northern Pakistan.

Officials initially said the powerful, 7.6-magnitute temblor killed at least 2,000 people. But the toll was widely expected to rise, and by Sunday morning, the Pakistani army's top spokesman said the military believed more than 18,000 people had perished, according to news services. He said 41,000 people had been injured.

"It is a national tragedy," Maj. Gen. Shaukat Sultan told reporters. "This is the worst earthquake in recent times."

The quake rattled dinnerware and nerves from Kabul to New Delhi, sending panicked city dwellers tumbling into streets where trees and utility poles danced and the pavement swayed sickeningly underfoot. Aftershocks continued throughout the day and were felt as far away as Bangladesh.

From all indications Saturday night, the earthquake visited its worst effects on the isolated towns and villages of Pakistan-controlled Kashmir and adjacent areas, where the dead included 250 girls who were crushed when their school in the Mansehra district collapsed and 200 army soldiers on duty, officials said. Entire villages were reportedly destroyed, and landslides blocked major roads. The army rushed troops and heavy equipment to the area to help with rescue operations.

More than 300 people were reported to have died on the Indian side of Kashmir, where hundreds of mud-and-stone homes were destroyed or buried under heaps of mud. A police official in the area, Ashoor Wani, told the Reuters news agency that the death toll would probably rise because many villages had been cut off by landslides.

The damage was as random as it was widespread. Here in the Pakistani capital, about 60 miles south of the epicenter, the temblor caused the collapse of a 10-story luxury high-rise but largely spared the rest of the city, despite shaking so violent that water sloshed over the edges of hotel swimming pools.

At the wrecked building, by nightfall rescuers wielding sledgehammers alongside backhoes, cranes and other heavy equipment worked frantically beneath the glare of floodlights to free scores of people believed still trapped in layers of twisted steel and concrete, part of which was streaked with blood. They paused periodically to listen for voices.

"We apprehend there could be anywhere from 70 to 100 people" still inside, said Iftikhar Ahmad, the inspector general of the Islamabad police, as several hundred army soldiers, police and volunteers swarmed over the rubble in a haze of dust. By 7 p.m., about 74 people had been rescued and eight bodies recovered, he said.

The earthquake struck at 8:50 a.m., at a depth of six miles, in the forested mountains of Kashmir near the Indian border, about 60 miles north of Islamabad, according to the Web site of the United States Geological Survey. The earthquake, which the survey described as "major," was followed by several smaller aftershocks that were felt as far away as Dhaka, the capital of Bangladesh, Reuters reported.

Officials said the earthquake was the worst to hit Pakistan since it was founded in 1947, according to the government's PTV television network.

The hardest-hit area appeared to be Pakistani Kashmir, where at least 1,000 people died, according to Mohammed Anwar, the top government official in the area. "That is my conservative guess, and the death toll could be much higher," he told Pakistan's Aaj television network.

Anwar and other officials said that few homes in Muzzafarabad, the capital of the area, had escaped damage, and schools, hospitals and other government buildings had collapsed. A military hospital in the garrison town of Rawalakot, also in Pakistani Kashmir, was reported destroyed.

With major roads blocked by landslides, the army dispatched troops by helicopter to some areas. Gen. Pervez Musharraf, Pakistan's president, told reporters during a visit to the collapsed high-rise in Islamabad that the air force would begin flying in supplies and rescuers by C-130 transport plane.

Aid organizations warned that relief efforts could be hampered by winter conditions that will soon prevail at the higher elevations of Kashmir. "Winterized tents and blankets will be urgently needed," Raphael Sindaye, Oxfam's humanitarian response coordinator, told Reuters reporters after a meeting of aid agencies in Islamabad.

India's prime minister, Manmohan Singh, offered his country's help. "While parts of India have also suffered from this unexpected natural disaster," he said in a message to Musharraf, "we are prepared to extend any assistance with rescue and relief which you deem appropriate." India and Pakistan have fought two wars over Kashmir but since early 2004 have been engaged in negotiations aimed at ending their historic enmity.

In Washington, Secretary of State Condoleezza Rice offered U.S. assistance to both countries. "At this difficult time, the United States stands with its friends in Pakistan and India, just as they stood with us and offered assistance after hurricane Katrina," she said in a statement.

Most of the deaths in Indian Kashmir occurred in villages near the cease-fire line that separates Indian and Pakistani forces in the province. About 130 people reportedly were killed in the remote town of Uri, situated on the highway that links the two sides of Kashmir. Many homes in the village were destroyed, and residents huddled in tents beneath a chilly drizzle, Reuters reported from the scene. About 40 Indian soldiers in the area also died.

The death toll may have been compounded by the calendar. This week marked the beginning of Ramadan, the Muslim holy month of prayer and fasting. As a result, many Pakistanis were asleep when the earthquake struck, having risen before dawn to pray and have a light meal in preparation for the daylong fast, then gone back to bed.

"It was really scary," said Najam Uddin, 30, a hotel clerk who lives in the nearby city of Rawalpindi. He had just woken up and was still lying in bed when he noticed that the house he shares with his parents was "shivering just like this," he said, waving his arms back and forth like sea grass in a current. His bed shook violently as books spilled from shelves and dinner plates shattered on the kitchen floor, he recalled.

The collapsed apartment building in Islamabad, the Margalla Towers, consisted of 40 apartments, according to Ahmad, the Islamabad police official. Some residents felt the initial tremors and managed to get out in time.

"The quake jolted me awake, and I saw people running down the staircase," one resident, Sabahat Ahmed, told Reuters. "By the time the second tremor hit, the building had already started to collapse. As the building was collapsing, people were still coming out from it."

But Sannia Hussain, a teacher from Lahore who was watching the rescue effort Saturday night, said her aunt and uncle were not so lucky. They had gone back to bed after rising early to pray and eat a pre-dawn meal in observance of Ramadan. Their daughter, a university student, had left the apartment to attend class. She raced home immediately after the earthquake "to find it was not there," said Hussain, 39.

A few hours later, a rescue worker found her aunt's cell phone in the rubble and called a number in it. The rescuer reached the woman's son, who lives with Hussain in Lahore. That triggered Hussain's journey to Islamabad. "Since then, we have heard nothing," she said.

Rescuers work at the site of a collapsed 10-story luxury high-rise in Islamabad, 60 miles south of the epicenter. Kashmiris wait with injured children to be airlifted to India from Uri, a town where 130 people died near the line between the two sides of disputed Kashmir.