"Our air defence systems thwarted an Israeli missile aggression on Damascus International Airport", Syrian regime news agency SANA cited a military source as saying.
Israel's Channel 2 reported that Israeli jets also hit weapon stores at the airport hangars. According to the report, several Israeli missiles were intercepted by Syrian air defenses.
He had no immediate information on casualties.
While Russia does not seem to have accepted Israel's demand for Iran to be completely removed from Syria, it has agreed to force the Islamic Republic's forces and proxies to leave the areas closest to the border with Israel.
Israel's air force has struck scores of targets it describes as Iranian deployments or arms transfers to Lebanon's Iran-backed Hezbollah movement in the war.
The Syrian News Agency (SANA) confirmed that Israel bombed the Damascus airport on Saturday evening. A statement by the Syrian Arab Army posted to Facebook stated, "We have reports of a large flaming mass being seen after it was shot down, but we can not yet confirm whether a jet was shot down or not".
Seven years since the last vote, the conflict has killed more than 360,000 people, forced millions more to flee, and left the economy in tatters.
Syrian troops now control around two-thirds of the country after scoring a series of military victories in recent months, including around Damascus and in the country's south.
Syrian troops have amassed around the opposition bastion for weeks, although an expected assault appears to be on hold for now as regime ally Russian Federation and rebel backer Turkey try to hash out a deal on Idlib.