After Trump announced the USA withdrawal from the deal on Tuesday, Rouhani warned that Iran would resume uranium enrichment at an even higher rate if the accord collapses.
The US, UK, France, Germany and a host of other countries including, unusually, Bahrain have affirmed Israel's right to defend itself against Iranian aggression.
A Britain-based war monitor, the Syrian Observatory for Human Rights, said the strikes killed at least 23 military personnel, including Syrians and non-Syrians.
"The Zionist regime can not stand peace and stability in the region and sees its own safety in making the region all the more unstable", Iranian Foreign Ministry spokesman Bahram Qasemi said, according to Iran's official Press TV.
Israeli Prime Minister Benjamin Netanyahu said Iran had "crossed a red line" and that Israel's bombardment against targets in Syria "was a effect". "Get rid of the Iranians and we can, perhaps, change our mode of life here", he said.
The heightened tension comes in the wake of the announcement by President Donald Trump that the United States would pull out of the global deal with Iran.
The Trump administration cast its hard line against the Iranian nuclear deal as a response, in part, to Tehran's military interventions in the region.
On Thursday, the White House condemned Iran's rocket attacks but failed to mention Israel's strikes on military targets in Syria.
The Quds Force, an external arm of Iran's Revolutionary Guards, carried out the rocket salvo, Israel said. Israel has called on the United Nations to immediately condemn Iran's attack.
Bahrain is a close ally of Saudi Arabia and the two countries, whose foreign policies are often in lockstep, are known for supporting Takfiri groups fighting to topple the Syrian government. Within Iran, it could empower hardliners while weakening the moderate camp that has sought better relations with the West.
Price solid in return as Red Sox beat Blue Jays, 5-2
Outfielder Dalton Pompey was optioned to Triple-A Buffalo. "Hopefully it's the first of many", Alford said of his first RBI. Xander Bogaerts stroked his fourth homer leading off the fourth for Boston to tie the game, and that should have been it.
Iran says Israel's rocket attacks on Syria were based on "invented pretexts".
"We hit nearly all of the Iranian infrastructure in Syria", Israeli Defense Minister Avigdor Liberman said Thursday at the Herzliya Conference, a security and defense convention. He added, "I hope that we ended this chapter and that everyone understood".
During the operation, about 50 Iranian targets were attacked in Syria, reaching intelligence positions, outposts, headquarters and equipment storage facilities in 16 different locations across the country.
Thursday's exchange followed a suspected Israeli rocket strike in Syria on Tuesday on a military base in Kisweh, hours after Trump's announcement on the nuclear deal.
Europe is already reeling from Trump's withdrawal from the Iran nuclear deal, which threatens European businesses who now face U.S. sanctions if they continue trading with Tehran. A commander in the pro-Syrian government regional alliance said there were no casualties. Israel has not confirmed or denied involvement.
The scope of the attacks, which Israel called its largest in Syria since 1973, raised the spectre of a conflict between Iran and Israel.
Syria's state news agency SANA said opposition fighters who made a decision to stay in the suburbs of Babila, Beit Sahem and Yalda will hand over the weapons and return to normal life.
The scale of Israeli rocket fire appeared to be far higher than in previous incidents and Damascus residents described seeing explosions above the city from air defence systems.