"Our air defence systems thwarted.an Israeli air aggression.and prevented it from achieving any of its goals", the source told state news agency SANA.
Israel's military said it had intercepted a rocket fired from Syria on Sunday, shortly after Damascus accused Israel of carrying out air strikes on its territory.
Damascus' air defense systems earlier on Sunday repelled an air strike by Israel in the south of Syria, a source in the country's military told Sputnik.
The Israeli military later said its Iron Dome interceptor system shot down a rocket fired at the northern part of the Golan Heights on the Syria frontier. A Syrian L-76 cargo lifter from Tehran was also en route to Damascus on Sunday morning.
Prime Minister Benjamin Netanyahu acknowledged an Israeli attack last week on what he called an Iranian arms cache in Syria, where Tehran provides Damascus with vital support.
The military statement did not specify where the rocket had been launched from. He also admitted that Israel carried out a strike overnight to January 12 at a warehouse storing weapons at the worldwide airport of Damascus.
"We have a fixed policy: to undermine Iranian entrenchment in Syria and to harm anyone who tries to harm us". SANA reported that "over eight targets" exploded over the capital, adding that most of the Israeli missiles had been intercepted.
Syrian state media broadcast footage of what it said were the air defenses firing, with bright lights seen shooting across the night sky. No damage or casualties on the ground were reported.
Israel has pledged to stop its main enemy Iran from entrenching itself militarily in neighbouring Syria.
On Sunday morning, three Syrians were killed in a auto bomb explosion at the entrance to an army camp in southern Damascus. Explosions were heard in one of the videos.