Unprecedented clashes between Israel and Iran over Syria have sparked calls for restraint from world leaders worried about the risk of all-out war, even as both sides said they want to avoid a regional conflict.

Israel carried out widespread deadly raids on Thursday against what it said were Iranian targets in Syria in response to rocket fire toward its forces that it blamed on Iran.

The reported exchange of fire came after weeks of rising tensions.

The bombardment led to calls for calm from Russia, France, Germany, Britain and the European Union, while the United States put the blame squarely on Iran and stressed Israel's right to "self-defense".

Moscow hopes that Iran and Israel will exercise restraint after alleged mutual missile attacks, a Kremlin spokesman said on Thursday.

"Moscow is concerned about the growing tensions and hopes that all parties will show restraint and resort exclusively to political and diplomatic means to solve all existing problems," Dmitry Peskov said.

Germany and Britain joined the US in denouncing the rocket fire toward the Israel-occupied Golan Heights they also said was carried out by Iran, while France reiterated its "unwavering support for Israel's security".

UN Secretary-General Antonio Guterres urged an immediate halt to "all hostile acts" to avoid "a new conflagration" in the Middle East.

Israeli Prime Minister Benjamin Netanyahu said Iran had "crossed a red line" and that the resulting bombardment against targets in Syria "was a consequence".

Iran's President Hassan Rouhani told German Chancellor Angela Merkel in a telephone call that he did not want "new tensions" in the Middle East.

Rouhani did not mention Israel's strikes in Syria, or those against the Israeli-occupied Golan Heights.

But the chairman of his country's parliamentary committee on foreign affairs, Allaeddine Boroujerdi, condemned the strikes, warning that "Israel has entered a dangerous game".

The Israeli raids in Syria, which a monitor said resulted in 23 deaths, constituted one of its largest military operations in recent years and the biggest such assault on Iranian targets, the Israeli military said.

"We hit nearly all the Iranian infrastructure in Syria," Defence Minister Avigdor Lieberman said.

"I hope we've finished this episode and everyone understood."

Israel carried out the raids after it said 20 rockets were fired from Syria at its forces in the Golan Heights at around midnight.

It blamed Iran's Quds force, adding that Israel's missile defense system intercepted four while the rest did not land in its territory.

If confirmed, it would be the first time Iran has sought to directly attack Israeli-controlled territory aside from an alleged attempted drone assault in February.

AP, Xinhua and AP contributed to this story.