Syria said two civilians were killed in the Israeli strikes.
Israelis are increasingly frustrated by nearly a year of government gridlock at time of rising tensions in the region. The strikes were in retaliation for four rockets fired at Israel from Syria the day before. Last week, Israel killed a senior commander of the Palestinian Islamic Jihad, an Iran-backed group in the Gaza Strip, setting off two days of heavy fighting. It said that the attack did not hit any Israeli communities.
The death toll was reported by Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, an opposition activist group with a network of contacts across Syria.
Video footage from Syria showed an errant Syrian air defense missile crashing into a heavily populated civilian area after launching, which reports indicate may have been to blame for some of the casualties.
The Observatory said that several other areas were targeted, including the Mazzeh airbase in western Damascus where air defence units are stationed.
"And Immediately our air defense systems thwarted the attack, intercepted the hostile missiles and downed majority before they reached their targets", Syria's official SANA news agency said on Tuesday night, quoting an unnamed military source.
SANA cited a military source that said: "At 1:20 AM, Israeli military warplanes fired several missiles from over both the Occupied Golan and Marj al-Eyoun in Lebanon targeting the outskirts of Damascus".
Israel has conducted hundreds of airstrikes in Syria throughout the eight-year conflict, a lot of them against what it says were targets of Iranian-backed militia groups such as the Lebanese Hezbollah.
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The protesters, meanwhile, made gains on a legal front when the high court struck down the ban on face masks. The city's hospital authority reported 221 injuries over the past day, with 12 people in serious condition.
The Israeli army has in the past targeted Shiite militias, including operatives from the Quds Force, which it says were responsible for attacks from Syria aimed at Israel.
Satellite image showing the destruction caused by Israeli airstrikes to an alleged Iranian-controlled facility at the Damascus International Airport on November 20, 2019.
"Four rockets were fired at us", said the statement on Twitter, adding that they were "intercepted by Iron Dome [air defense] batteries".
A war monitoring group says Israeli airstrikes in Syria early this morning killed 11 people, including seven non-Syrians who are most likely Iranians.
"I have made it clear that whoever hurts us - we will hurt him". We conducted an expedited battle procedure, along with a series of air force strikes we carried out tonight.
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Israel's new hard-line defence minister, Naftali Bennett, issued an equally firm statement. Our message to Iran's leaders is simple: You are no longer immune. "Wherever you send your octopus tentacles, we will hack them off".
The rare rocket fire comes a week after an Israeli airstrike against a top Palestinian militant based in Syria. The militant, Akram al-Ajouri, survived the attack but his son and granddaughter were killed. In Gaza, it supplies Islamic Jihad with cash, weapons and expertise.
Israel was responding to rockets it said were fired in its direction by Iranian forces in Syria the previous night.