Israel says it has struck almost all of Iran's military infrastructure inside Syria in its biggest assault since the start of the civil war there.
The strikes came after 20 rockets were fired at Israeli military positions in the occupied Golan Heights overnight.
Syria's military said the Israeli "aggression" had killed three people.
There was no immediate comment from Iran, whose deployment of troops to Syria to help President Bashar al-Assad has alarmed Israel.
Iran has repeatedly called for an end to the existence of the Jewish state.
Russia, Germany and France called on both countries to exercise restraint, but the US said Iran bore "full responsibility for the consequences of its reckless actions" and that Israel had a right to defend itself.
What happened in the Golan?
The Golan Heights is a rocky plateau in south-western Syria, about 50km (30 miles) from the capital Damascus. Israel occupied most of the area in the 1967 Middle East war and later annexed it in a move not recognised internationally.
The Israel Defence Forces (IDF) said that early on Thursday morning 20 rockets had been launched at its forward posts there by the Quds Force, the overseas operations arm of Iran's Islamic Revolution Guards Corps.
IDF spokesman Lt Col Jonathan Conricus said four rockets were intercepted by the Israeli Iron Dome aerial defence system, while 16 others fell short of their targets. No injuries or damage were reported.
The Syrian Observatory for Human Rights, a UK-based monitoring group, confirmed that rockets were fired towards the occupied Golan. But it said the attack came after Israeli forces bombarded Baath, a town in the demilitarised zone.
A senior source in an Iranian-led military alliance that supports Syria's government also told AFP news agency that Israeli forces had fired first.
How did Israel respond to the rocket fire?
Col Conricus said fighter jets had struck 70 military targets belonging to Iran inside Syria, causing significant damage. The targets included:
- Intelligence sites associated with Iran and its proxies
- A logistics headquarters belonging to the Quds Force
- A military logistics compound in Kiswah, a town south of Damascus
- An Iranian military compound north of Damascus
- Quds Force munition storage warehouses at Damascus International Airport
- Intelligence systems and posts associated with the Quds Force
- Observation and military posts and munitions in the Golan demilitarised zone
The IDF said it had also targeted Syrian military air defence systems after they fired at the fighter jets despite an Israeli "warning".
Israeli Defence Minister Avigdor Lieberman later told a conference in the town of Herzliya that the IDF had "hit almost all of the Iranian infrastructure in Syria".
"They must remember that if it rains here [in Israel], it will pour there," he said. "I hope that we have finished this chapter and that everyone got the message."
However, Syria's military declared it had "thwarted a new Israeli act of aggression" and that its air defences "destroyed a large part" of the missile barrage.
Three people were killed by the missiles, a spokesman said. A radar station and an ammunition depot were also destroyed, and several air defence bases sustained damage, he added.
The Syrian Observatory reported that at least 23 people were killed, including five Syrian soldiers and 18 other allied fighters.
Russia, which is also supporting the Syrian military, said Israel fired 60 air-to-surface and 10 surface-to-surface missiles and that more than half were shot down.
'No-one wants an all-out war'
By Jonathan Marcus, defence correspondent, BBC News
These events have tactical and strategic dimensions.
In the short-term the Iranians are seeking "pay back" for an Israeli strike against one of their bases in Syria a little over a month ago. On Wednesday night, according to the Israeli military, Iran's Quds Force launched rockets against Israeli positions in the Golan Heights.
But the scale of the attack was limited - a single multiple-barrel rocket launcher appears to have been used, which the Israelis say they subsequently destroyed. They then apparently hit every Iranian facility they know of in Syria to send a powerful message to Tehran.
But neither Israel nor Iran appear to want an all-out war at this stage.
Nonetheless their strategic rivalry is clear. Tehran is seeking to establish itself as a military player in Syria to open up another potential front against Israel. And Israel is equally determined to prevent this.
Why is Israel so worried about Iran's activities in Syria?
Israel's military had been anticipating an attack by Iranian forces after reportedly carrying out a number of strikes on their facilities in Syria in recent months. They included one on an airbase in April that killed seven Iranian troops.
Israeli officials have repeatedly warned that they are determined to stop what they consider Iranian "military entrenchment" in the country.
Iran has deployed hundreds of troops, ostensibly as military advisers to the Syrian military. Thousands of militiamen armed, trained and financed by Iran have also been battling rebel forces alongside Syrian soldiers.
Earlier this week, Israeli Prime Minister Benjamin Netanyahu said the Revolutionary Guards had moved advanced weapons to Syria, including surface-to-surface missiles and anti-aircraft batteries that would threaten Israeli fighter jets.
Mr Netanyahu's lobbying against the 2015 nuclear deal between Iran and six world powers, which US President Donald Trump abandoned on Tuesday, has raised tensions further with Tehran.
Mr Lieberman stressed that while Israel had "no interest in escalation", it had to "be prepared for any scenario". "We are facing a new reality where Iran is attacking Israel directly and trying to harm Israel's sovereignty and territories," he added.