Most passengers on the flight from the western city of Herat were Afghans but 19 foreigners are also believed to have died. They included three US aid workers, an Italian naval officer, nine Turkish road engineers, and six Russian air crew.
The cause of the crash was unclear with conflicting accounts of events before the aircraft disappeared from radar screens. Shah Mahmoud Miakhel, the deputy interior minister, told Reuters: "It did not have so much fuel to enable it to fly far, so it may have crashed." Zimarai Kamgar, president of Kam Air, said the plane had been given clearance to land at Peshawar in Pakistan after it was turned away from Kabul.
But the transport minister Enayatullah Qasemi later said the plane had been given clearance to land at Kabul by air traffic controllers at the US base in Bagram, who control Afghan airspace. He said the pilot last contacted the Kabul control tower at 3pm on Thursday to ask for a weather update and was cleared for landing by Bagram, moments before it disappeared from radar screens three miles from the city.
The transport minister said officials checked with local airfields and those in neighbouring countries but there were no reports of the plane.
Hopes of finding survivors were slim. An apparent crash site was found by Nato search aircraft but could not be checked before nightfall. Troops tried to reach the site by helicopter but the search was suspended because of freezing fog. There was no signal from the plane's rescue beacon.
Weather conditions were severe on Thursday when Afghanistan suffered some of the worst snowstorms in living memory, bringing Kabul to a virtual close and cutting the main road to Pakistan.
Afghanistan's airline industry has expanded in the past year but most foreign aid workers and diplomats are banned from Afghan aircraft and the capital's airport is regarded as one of the riskiest anywhere, although it has a vital role as Kabul's lifeline to the outside world.
Foreign airlines complain privately of limited air traffic control services, poor-quality aviation fuel, runway surfaces that are so rough they damage undercarriages, and challenging flying conditions caused by Kabul's high altitude and the mountains surrounding the city.
Several foreign airlines have abandoned plans to begin services to Afghanistan after visiting the airport, which until recently had uncleared minefields alongside runways and was littered with dozens of wrecked aircraft from 20 years of war.
Afghan aircraft have long had a poor safety reputation. In 1998 a Boeing 727 from the national carrier Ariana Airlines crashed in the same area of mountains as Thursday's accident, killing 45 people, and another Ariana flight crashed in Pakistan the same year killing 51.
Afghans call planes from the country's national carrier Ariana "the coffins that fly" and aid workers nicknamed the airline "Air Inshallah" (Air God Willing). Officials last year admitted they had bought no spare parts for months because of lack of funds.
Kam Air was Afghanistan's first private airline and was generally better regarded by expatriates and Afghans, many of whom preferred its relatively cheap fares to risking long, bumpy journeys on dangerous roads notorious for accidents and banditry.
It started flying last year, operating a fleet of leased Boeing and Antonov planes on Afghan routes and to Dubai and Istanbul. It suffered an accident in September when a plane skidded off a runway at Kabul, injuring several passengers.