The victims died when the plane crashed yesterday in the town of Ariha in Idlib province, and in preceding air strikes, according to the Syrian Observatory for Human Rights, which originally said 31 were killed.
"There are three children among the 37 victims," the Britain-based monitor said.
The crash and explosion destroyed the main market in Ariha, which was overrun by a rebel Islamist alliance in May.
Local activist Ibrahim al-Idlibi, speaking to AFP via the Internet, said the blast was caused by rockets and bombs still on the plane.
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The Damascus regime has relied heavily on its monopoly of air power in Syria's four-year-long civil war, repeatedly pounding rebel-held towns.
It has lost a number of aircraft, some to rebel fire and others to mechanical failure.
In mid-January, at least 35 government troops were killed when a military aircraft crashed in Idlib.
The province, which borders Turkey, has since been largely overrun by a rebel alliance including Al-Qaeda affiliate Al-Nusra Front.