NEW DELHI — A powerful earthquake shook Nepal on Saturday near its capital, Katmandu, killing more than 1,900 people, flattening sections of the city’s historic center, and trapping dozens of sightseers in a 200-foot watchtower that came crashing down into a pile of bricks.

As officials in Nepal faced the devastation on Sunday morning, they said that most of the 1,931 deaths occurred in Katmandu and the surrounding valley, and that more than 4,700 people had been injured. But the quake touched a vast expanse of the subcontinent. It set off avalanches around Mount Everest, where at least 17 climbers died. At least 34 deaths occurred in northern India. Buildings swayed in Tibet and Bangladesh.

The earthquake, with a magnitude of 7.8, struck shortly before noon, and residents of Katmandu ran into the streets and other open spaces as buildings fell, throwing up clouds of dust. Wide cracks opened on paved streets and in the walls of city buildings. Motorcycles tipped over and slid off the edge of a highway.

By midafternoon, the United States Geological Survey had counted 12 aftershocks, one of which measured 6.6.