Syria's armed forces said insurgents downed a military jet in northern Hama province on Tuesday, killing the pilot.
Militant group Tahrir al Sham - a fighting force dominated by members of Al Qaeda's former branch in Syria - said it hit the plane.
A source said the militants were searching for another pilot they believed had survived the crash.
Syria's air force and army, supported by Russian air power and Iranian-backed militias, have stepped up an offensive in Hama in recent weeks, pushing north towards the rebel stronghold of Idlib.
Aid workers and witnesses say dozens of civilians have been killed in towns and villages away from the front lines.