"The Su-24 plane rolled off the runway and broke up while accelerating for takeoff... The plane's crew did not have time to eject and died," the spokesman said.
He did not clarify how many people died, but the Su-24 usually has a crew of two.
"According to a report from the scene of the accident, the reason could be a technical failure," he added.
Russia has staged air strikes in Syria in support of the regime of President Bashar al-Assad since 2015.
The latest casualties put the toll of Russian servicemen officially reported killed in Syria at 37.
Last month a Russian general was killed near the eastern city of Deir Ezzor, where Russian special forces are participating in the regime's ground offensive.