The rebel Free Syrian Army (FSA) say they shot a military aircraft down near the Iraqi border.
But state media say the plane crashed because of “technical problems” and a search is under way to find the pilot.
Government forces have continued their advance in Aleppo, with reports of clashes in the west of the city.
According to Syria’s state-run news agency Sana, the plane that went down had suffered a fault with its “control mechanisms” during a routine training mission, forcing the pilot to abandon the aircraft.
The aircraft was shot down near the town of al-Muhassan, around 120 km (75 miles) from the Iraqi border in Deir al-Zour province, the rebels say.
The FSA says that one of the two-man crew died and that another has been captured.
A group calling itself the “Revolutionary Youth of the Land of the Euphrates” uploaded a video to YouTube purporting to show the captured pilot surrounded by three armed rebels, saying that his mission was to “bomb the town of al-Muhassan”.
In the video, which cannot be independently verified, the seemingly middle-aged man identifies himself as a pilot, Col. Fareer Mohammad Suleiman. He appears to have minor bruising to his face which he attributes to the plane crash.
In other footage provided by the rebels, what appears to be a Russian-built MiG-23 fighter jet is shown carrying two under-wing weapons pods thought to be loaded with air-to-ground missiles.
Anti-aircraft fire can be heard before the jet bursts into flames.
Rebel gunners are then heard on the footage celebrating.
If the rebels have succeeded in downing a MiG-23, it would be a significant moment in the conflict.
Reports have emerged recently of anti-aircraft weapons reaching rebels in Syria.
Earlier this week, photos were posted online by rebels showing them with a full surface-to-air missile system. This would pose a potential threat to the regime’s air power, correspondents say.
Meanwhile, activists say government forces have begun a new advance against rebels in Aleppo, Syria’s largest city. Aleppo has seen fierce clashes between the two sides in recent weeks.
Government forces entered the Saif al-Dawla neighborhood with tanks and armored vehicles, according to the UK-based Syrian Observatory for Human Rights.
The strategic northern district of Salah al-Din had been coming under bombardment since the morning, the Observatory said.
State media also said Syrian armed forces in central Homs province had killed a large number of “mercenary terrorists”.
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