A police official said the death toll in Nepal alone had reached 876, more than half of them in the Kathmandu Valley.
A further 34 fatalities were reported in northern India and one in Bangladesh, and the estimate for the total number of fatalities now exceeds 1,500.
The shallow earthquake toppled buildings and opened gaping cracks in roads.
Devyani Pant, an Indian tourist, told Reuters she was in a Kathmandu coffee shop with friends when “suddenly the tables started trembling and paintings on the wall fell on the ground”.
“We are now collecting bodies and rushing the injured to the ambulance,” she said. “We are being forced to pile several bodies one above the other to fit them in.”
At least 10 people were killed when an avalanche triggered by the earthquake hit the Everest base camp, a tourism official said, where more than 1,000 climbers had gathered for the start of the annual climbing season.
Mohan Krishna Sapkota, another tourism official, said it was “hard to even assess what the death toll and the extent of damage” around Everest could be.
“The trekkers are scattered all around the base camp and some had even trekked further up,” he added. “It is almost impossible to get in touch with anyone.”
About 300,000 foreign tourists were estimated to be in various parts of Nepal for the spring trekking and climbing season in the Himalayas.
Rescuers scrabbled through the rubble of destroyed buildings across the capital, among them ancient, wooden Hindu temples.
Aftershocks continued throughout the afternoon, with many residents choosing to stay out in the streets.