Officials in Pakistan last night said nearly 20,000 bodies had been counted, but estimated the toll could exceed 30,000.
The vast majority of the deaths from Saturday's magnitude 7.7 quake were in Pakistan. Rival India, which reported hundreds dead, offered assistance.
More than 30,000 people, many of them students, were estimated to have died in the Pakistan-controlled portion of Kashmir, said the region's communications minister, Tariq Mahmmod.
"I have been informed by my department that more than 30,000 people have died in Kashmir," he said.
The worst-hit city was Pakistani Kashmir's capital, Muzaffarabad, where 11,000 died, said Pakistan's interior minister, Aftab Khan Sherpao.
Authorities in India reported 600 deaths and more than 900 people injured, while Afghanistan reported at least four deaths. The quake, centred in Pakistani Kashmir, flattened dozens of villages. It killed farmers, soldiers and schoolchildren, and triggered landslides that blocked rescuers from many areas where bodies lay in streets and villagers said they felt forsaken.
Many survivors were left without shelter in nearfreezing night- time temperatures.
In India's portion of Kashmir, villagers burned wood from their own collapsed homes for warmth.
Mr Mahmmod said the army was providing help to survivors only in Kashmir's major cities and towns, and "they (troops) have not started relief work in remote villages where people are still buried in the rubble, and in some areas nobody is present to organise funerals for the dead".
Two survivors were pulled yesterday from a destroyed apartment building in Pakistan's capital, Islamabad.
"We are handling the worst disaster in Pakistan's history," said Major General Shaukat Sultan, the country's top military spokesman.
"We do seek international assistance," said Pakistani president General Pervez Musharraf. "We have enough manpower, but we need financial support."
The quake and its aftershocks were felt from central Afghanistan to western Bangladesh. Buildings were wrecked in an area spanning at least 250 miles, from Jalalabad in Afghanistan to Srinagar in northern Indian territory.
Rescuers pulled two survivors - a boy and a woman - from a collapsed apartment building in Islamabad. Others were trapped alive, according to Adil Inayat, a doctor in Islamabad.
"These people heard voices and cries during the whole night," Inayat said. At least 24 people died.