However, Air India was able to operate two flight in the morning, one each from Delhi and Kolkata with 118 and 45 passengers on board.
The two flights returned with 135 and 45 passengers, an Air India spokesperson said.
Air India operates three services to Kathmandu including two daily services from the national capital. The Kolkata-Kathmandu-Kolkata flight is, however, operated four times a week.
Besides Air India, other domestic carriers had also cancelled their services to Kathmandu.
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A SpiceJet spokesperson said that the airline was awaiting clearance from the Nepalese aviation authorities to resume the services adding, "We plan to combine the two flights and operate them as one later today depending on the situation."
SpiceJet operates two daily services to Kathmandu from the national capital.
A magnitude 6.7 aftershock shook the Kathmandu area of Nepal a day after the massive earthquake devastated the region, killing hundreds of people.