The Syrian Observatory for Human Rights said the plane crashed after hitting electricity lines in heavy fog in Idlib province, a claim echoed by Syrian state media.
But Syria's Al-Qaeda affiliate Al-Nusra Front claimed on Twitter that it had shot down the aircraft.
Syrian state media reported the crash without giving a death toll.
"A medium-sized cargo plane crashed last night while landing at the Abu al-Duhur military airport because of bad weather conditions and heavy fog, killing the crew on board," state news agency SANA said.
The Observatory said regime forces were involved in heavy clashes with Al-Nusra fighters in a bid to reach and recover the bodies of those killed in the crash.
On one of its Twitter accounts, Al-Nusra claimed it had shot down the plane and posted photos it said showed some of those killed in the crash, as well as the remains of the aircraft.
Militant groups have regularly shot down regime planes and helicopters in the country's civil war.
In December, Islamic State group militants shot down a Jordanian plane participating in an international coalition against the jihadist organisation and captured its pilot.
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