Lieutenant Colonel Jonathan Conricus, an Israeli military spokesman, said earlier that Iran's Al Quds force fired the rockets at several Israeli bases, though he would not say how Israel determined the Iranian involvement.
The incoming attack set off air raid sirens in the Israeli-controlled Golan, which was captured from Syria in the 1967 war.
Israel "views this Iranian attack very severely," Conricus told reporters. He said Israel had responded, but did not provide details. "This event is not over," he said.
Syria's state media said Syrian air defences had intercepted "hostile Israeli missiles" that were fired over southwestern Damascus.
Hours later, state-run Al-Ikhbariya TV broadcast a live feed of Syrian air defences firing into the sky above the capital, and loud explosions and air defence firing were heard through the night.
Syrian activists reported Israeli airstrikes hitting targets near Damascus.
One video posted online showed a large explosion and shrapnel flying in the air.
Residents reported loud sounds that rocked their buildings. It was not immediately clear what was hit.
An Israeli army spokesman, Avichay Adraee, said on Twitter that Israel was "acting against Iranian targets inside Syria," a rare admission by an Israeli official.
Al-Ikhbariya TV said Israel also targeted military posts in southern Suweida province, including an air base, and struck near Homs in central Syria. The state TV station said the attacks were foiled.
Syrian media earlier said the hostilities began with Israeli fire at Syrian positions in southern Syria from across the border. Pro-Syrian media said Syrian missiles then fired at Israeli forces.
One TV station, Beirut-based Al-Mayadeen, said at least 50 missiles were fired from Syria at Israeli forces in the Golan Heights.
Al-Ikhbariya TV said missiles targeted 10 Israeli positions.
Syrian media said it was the first time in years that Syrians had fired at Israeli forces in the Golan Heights.
Israel has been on heightened alert in recent days, anticipating an Iranian attack following Iranian vows to retaliate to what it says are recent Israeli strikes in Syria targeting Iranian outposts.
Yesterday, Syrian state media said Israel struck a military outpost near the capital of Damascus. The Britain-based Syrian Observatory for Human Rights said the missiles targeted depots and rocket launchers that likely belonged to Iran's elite Revolutionary Guard, killing at least 15 people, eight of them Iranians.
Last month, an attack on Syria's T4 air base in Homs province killed seven Iranian military personnel.
On April 30, Israel was said to have struck government outposts in northern Syria, killing more than a dozen pro-government fighters, many of them Iranians.
Israel has neither confirmed nor denied most of the airstrikes. But for months, it has repeatedly said it will not accept a permanent Iranian military presence in Syria.
In February, Israel shot down what it said was an armed Iranian drone that entered Israeli airspace. Israel responded by attacking anti-aircraft positions in Syria, but an Israeli warplane was shot down during the battle.
Iranian forces moved into Syria after the outbreak of the Syrian civil war in 2011 to back the forces of President Bashar al-Assad. As that war winds down, and Assad appears to be headed toward victory, Israel fears that Iran, along with tens of thousands of Iranian-backed Shia militiamen, will carry out attacks against Israel.
US President Donald Trump's announcement yesterday that the US was withdrawing from the 2015 nuclear deal with Iran has triggered uncertainty and threatened to spark more unrest in the Middle East.
-AP
