TEHRAN — Southeast Iran was hit Tuesday by the most powerful earthquake to strike the country in 40 years, and its reverberations were felt as far away as India, but Iranian officials said the tremor had originated so deep underground, and in such a sparsely populated area, that it caused relatively few casualties and only minor damage.

The authorities in Iran had initially feared hundreds of deaths from the 7.8-magnitude earthquake, but scaled back their assessment as it became clear that its depth, initially reported to be only about 10 miles beneath the surface, was more than 56 miles beneath. The shallower the quake, the greater the ground motion and potential for damage.

The earthquake, which struck at 3:14 p.m. local time, was felt in several countries, rocking buildings in the Indian capital, New Delhi, sending panicked residents of Karachi, Pakistan, fleeing into the streets and causing tremors through Persian Gulf states.

The United States Geological Survey said the earthquake’s epicenter was near Khash, Iran, not far from the border with Pakistan, in the Iranian province of Sistan-Baluchistan. The province, with vast expanses of unpopulated territory, is home to nearly two million people. Most are concentrated in Zahedan, the provincial capital, and the cities of Saravan and Khash.