They were near the airport and around the Kisweh area south of Damascus, said the Britain-based Observatory.
In an earlier report, SANA had spoken of Syrian air defence batteries attacking "enemy targets".
On Friday, Syrian state news agency SANA reported that the country's air defenses intercepted missiles fired at the Damascus worldwide airport at around 11:00 p.m. local time, with a military source attributing the attack to Israel.
In a statement published on Saturday, the ministry said it had dispatched letters to the secretary general of the United Nations and the head of the UN Security Council (UNSC) in connection with Friday night's unprovoked attack on Damascus.
Israeli drones and warplanes were heard flying Friday afternoon over Lebanon.
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Only a warehouse in the Damascus International Airport was damaged, according to the statement.
A Transport Ministry spokesperson told SANA that air traffic from the airport was unaffected by the conflict. However, the Arab country's air defense systems have thwarted most of the attacks.
Israel also insists that Iran uses Syria as a bridge to supply missiles and other weapons to Hezbollah in Lebanon. In 2017 the BBC, quoting a Western intelligence source, reported the Iranian military had reportedly established a compound at a site used by the Syrian army outside Al Kiswah, 14 km south of Damascus.
During the past few years, Israel has frequently attacked targets in Syria in what is considered as an attempt to prop up terrorist groups that have been suffering defeats in their fight against Syrian government forces.