In a rare confirmation of their operations in Syria, the Israeli army said they had carried out dozens of strikes against the Iranian elite Quds Force and the Syrian military, in response to four rockets fired at Israel a day before.

Britain-based monitoring group the Syrian Observatory for Human Rights (SOHR) said 23 people were killed in the strikes -- 21 fighters and two civilians.

Sixteen were non-Syrian fighters, the group's head Rami Abdel Rahman said.

Iran has fought alongside Syrian President Bashar al-Assad's forces in the country's eight-year civil war, heightening Israeli concern over the presence of its arch foe along its border.

"Whoever hurts us, we will hurt him," Israeli Prime Minister Benjamin Netanyahu said in a statement.

"This is what we did overnight vis-a-vis military targets of the Iranian Quds Force and Syrian military targets in Syria after a barrage of rockets was launched at Israel."

The Israeli army said they had targeted about a dozen military sites, including warehouses and military command centres.

"It was very intense," spokesman Jonathan Conricus told AFP.

The most important target, he said, was a control facility at the main international airport in Damascus.

"It is the main building that serves the (Iranian) Revolutionary Guards... for coordinating the logistic facilities of transport of military hardware from Iran to Syria and from Syria onwards," he said.

- 'Heavy attack' -

Israel has carried out frequent air and missile strikes against Iranian targets inside Syria since the country descended into civil war in 2011, but rarely comments on them.

On Tuesday, four rockets were fired at Israel from Syria, with the army blaming an "Iranian force".

Israel's Iron Dome missile defence system intercepted the rockets.

Conricus said it was the sixth time Iranian forces had tried to attack Israel directly in recent years, most recently in August.

The Israeli attack Wednesday began in the early hours, with a series of large explosions rocking Damascus, an AFP correspondent in the city said.

Syria's state news agency SANA said Syrian anti-aircraft defences responded to a "heavy attack" by Israeli warplanes over the capital.

The Israeli army confirmed missiles were fired towards its jets but denied any were hit.

In response to the fire, it said, "a number of Syrian aerial defence batteries were destroyed".

"We hold the Syrian regime responsible for the actions that take place in Syrian territory and warn them against allowing further attacks against Israel," the army said.

SANA added that the strikes were carried out from "Lebanese and Palestinian territories". Israel sometimes launches attacks on Syria from planes flying over neighbouring Lebanon.

Syria's civil war has been complicated by the involvement of multiple foreign powers, with Russian, Iranian and US forces on the ground backing various parties.

Russia, which has backed Assad's regime militarily, condemned the Israeli attack.

Russian Deputy Foreign Minister Mikhail Bogdanov was quoted by TASS news agency as saying the operation "totally contradicts international law".

"We are going to examine the circumstances, all this is very bad," he added.

- Flare-up -

The Observatory said Tuesday's rockets were fired from positions around the Syrian capital held by groups loyal to the Damascus government.

The flare-up follows a major escalation in and around the Palestinian enclave of Gaza last week when Israel killed a top commander of militant group Islamic Jihad, which is allied with Damascus.

The killing was accompanied by a second strike, unconfirmed by Israel, on an Islamic Jihad leader in Damascus that killed his son and another person, according to SANA.

The hundreds of strikes Israel has carried out in Syria have mostly been against Iranian targets or positions of Iran's Lebanese ally, Shiite militant group Hezbollah.

Both are sworn enemies of the Jewish state and have backed the Syrian president's forces.

The war in Syria has killed more than 370,000 people and displaced millions.