"Forty-nine people were killed in the incident. Now we are carrying out rescue operations," Bishwo Raj Pokharel, a senior police official involved in the rescue operation at TIA, told Xinhua news agency.
The 78-seater Bombardier Dash 8 aircraft, with 71 people on board, was flying from Dhaka to Kathmandu. It veered off the runway and caught fire while landing at 2.20 p.m., said TIA spokesperson Prem Nath Thakur.
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All flights in and out of the Tribhuvan International Airport were cancelled. The airport was reopened later.
Director General of Civil Aviation Authority of Nepal Sanjiv Gautam said the plane lost control when it attempted to land on the runway.
"The aircraft was permitted to land from the southern side of the runway flying over Koteshwor but it landed from the northern side," said Gautam, adding that the aircraft might have sustained technical glitches.
"We are yet to ascertain the reason behind the unusual landing," he said.
Photos and videos posted on social media showed smoke rising from the airport runway. Witnesses said the plane crashed when trying to take a sharp turn over the runway, My Republica reported.
"I saw the plane make a sharp turn over the terminal back towards south and then disappeared towards the runway. Then immediately a large plume of smoke was seen," said Arnico Pandey, adding that the plane was flying very low, just enough to be above the control tower.
A survivor, Nepalese travel agent Basanta Bohora, recounted from his hospital bed his experience during the fateful crash-landing.
After a normal take-off from Dhaka, the plane began to behave strangely as it approached Kathmandu, he said.
"All of a sudden the plane shook violently and there was a loud bang," he was quoted as saying by the Kathmandu Post.
"I was seated near the window and was able to break out of the window," Bohora said.
"I have no recollection after I got out of the plane. Someone took me to Sinamangal Hospital and from there my friends brought me to Norvic (Hospital). I have received injuries to my head and legs, but I am fortunate that I survived the ordeal."
Offering his condolences to the bereaved, Nepali Prime Minister K.P. Sharma Oli said he was "extremely shocked" by news of the crash and promised an immediate government investigation.
At least 33 Nepali passengers were on board the plane, according to officials. The US-Bangla Airlines is a privately-owned Bangladeshi airline headquartered in Dhaka.
This is the most severe air crash at Kathmandu's Tribhuvan International Airport after a Turkish Airlines flight crash-landed in March 2015.