The pilot ejected and landed near the town of Jayrud, 60 kilometres (35 miles) northeast of Damascus, it said.
The army, quoted by state news agency SANA, said the pilot landed in an area controlled by Jaish al-Islam rebels after his plane developed "a technical problem during an exercise".
"This crime committed by the terrorists of Jaish al-Islam will not go unpunished," it said.
The Saudi-backed rebel group claimed it had hit the plane -- identified as a Russian-made Sukhoi Su-22 -- and captured the pilot.
Jaish al-Islam's spokesman, Islam Alloush, posted a photo and a video of the pilot on his Twitter account, saying he belonged to the Alawite sect of President Bashar al-Assad.
He later said that a jihadist with Al-Nusra Front, Al-Qaeda's affiliate in Syria, had executed the pilot.
Several government aircraft have been shot down by rebels or crashed because of technical faults since Syria's civil war began five years ago.
The conflict has killed more than 280,000 people and displaced millions.
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The army, quoted by state news agency SANA, said the pilot landed in an area controlled by Jaish al-Islam rebels after his plane developed "a technical problem during an exercise".
"This crime committed by the terrorists of Jaish al-Islam will not go unpunished," it said.
The Saudi-backed rebel group claimed it had hit the plane -- identified as a Russian-made Sukhoi Su-22 -- and captured the pilot.
Jaish al-Islam's spokesman, Islam Alloush, posted a photo and a video of the pilot on his Twitter account, saying he belonged to the Alawite sect of President Bashar al-Assad.
He later said that a jihadist with Al-Nusra Front, Al-Qaeda's affiliate in Syria, had executed the pilot.
Several government aircraft have been shot down by rebels or crashed because of technical faults since Syria's civil war began five years ago.
The conflict has killed more than 280,000 people and displaced millions.
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