The Israeli army said in a statement on Sunday fighter jets "struck Islamic Jihad terror targets south of Damascus", following rocket fire from the Gaza Strip.
"In the Adeliyah region, outside of Damascus, an Islamic Jihad compound was struck, used as a hub of Islamic Jihad's activity in Syria," it added, while confirming a number of other attacks in Gaza.
It is rare for them to claim such attacks directly.
The Islamic Jihad operates in the Palestinian territories and Syria and fired more than 20 rockets from Gaza throughout Sunday.
An AFP correspondent in Damascus heard several strong explosions shortly before midnight local time (22:00 GMT).
The Syrian Observatory for Human Rights (SOHR) said the attacks were "near the Damascus international airport".
The Syrian state news agency SANA said "most of the enemy missiles were shot down before reaching their targets," stressing that "no airport" was struck.
Earlier, SANA said the anti-air defences were activated against attacks "in the Damascus area".
Since the start of the Syrian conflict in 2011, Israel has carried out hundreds of raids in Syria, mainly targeting government forces as well as allied Iranian forces and Hezbollah fighters.
A missile attack blamed on Israel in mid-February killed three Syrian and four Iranian fighters in the Damascus airport area, according to the SOHR.
Iran is an ally of Damascus and has offered military advisers and sent militiamen and material support to help President Bashar al-Assad's government forces in the nine-year civil war.
Israel considers Iran a national security threat and says it would not tolerate Iran's presence on its borders.
In November, Israel targeted two senior Islamic Jihad commanders in a simultaneous attack, killing one in the Gaza Strip and missing the second in Syria.
At the time, Israeli warplanes fired three missiles at the home of Akram al-Ajouri, a member of the Islamic Jihad's leadership living in exile. He was not harmed, but his son and granddaughter were killed.
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