The cross-border exchanges early on Sunday came as Israel escalates violence on multiple fronts, including in Gaza, Lebanon, occupied East Jerusalem and the occupied West Bank.
There was no immediate comment from the Syrian government.
The Israeli military said it had launched artillery attacks and a drone against the rocket launchers in Syria.
There were two rounds of rocket launches from Syrian territory in the early hours of Sunday, it said. The first involved three rockets, one of which landed in a field in the Israeli-annexed Golan Heights.
The second launch, which also involved three rockets, set off sirens in northern Israel. There were no reports of casualties. Jordan’s army said debris from a rocket fell into its territory but caused no casualties or damage.
Lebanon-based Al Mayadeen TV said the rocket launches were claimed by the al-Quds Brigades, the armed wing of the Palestinian Islamic Jihad movement.
The rocket fire from Syria comes against the backdrop of soaring Israeli-Palestinian tensions triggered by Israeli police raids on the Al-Aqsa Mosque compound in which police fired stun grenades and rubber-coated steel bullets at Palestinian worshippers gathered for Ramadan prayers.
The site in Jerusalem’s Old City, holy to both Muslims and Jews, who know it as Temple Mount, has been a longstanding flashpoint, notably over the issue of Jewish visitors defying a ban on non-Muslim prayer in the mosque compound.
The raids came at a time of heightened religious fervour – with Ramadan coinciding with the Jewish holiday of Passover and the Christian Easter celebrations. Violent scenes from the attacks outraged Palestinians observing the holy fasting month of Ramadan and prompted armed groups in Lebanon and the Gaza Strip to fire a barrage of rockets into Israel.
The Israeli military then bombed several sites that it said belonged to the Palestinian group Hamas in Gaza and southern Lebanon.
Gideon Levy, an Israeli journalist and author, told Al Jazeera that tensions between Israel and its neighbours were at a critical point.
“The situation is extremely explosive,” he said.
“Unlike the former years, we are facing a very radical government, which is one hand quite powerful, and on the other very fragile, because the most radical parts of it are pushing for action that might turn out into a catastrophe,” he said, referring to Israeli Prime Minister Benjamin Netanyahu’s ultra-nationalist government.
“The scenes from the Al-Aqsa Mosque were scenes not seen in recent years in their brutality and I think that any small match can set fire now to the whole area. Hopefully, it will not happen, but nobody can guarantee this will not happen,” he said.
Levy also noted Israel has been carrying out hundreds of attacks against what it says are Iran-linked groups in Syria, bombing ports and airports, including the main facility in Aleppo that had been a conduit for aid shipments since the deadly earthquakes that hit northern Syria and southern Turkey on February 6.
“There is no public argument about this [raids in Syria] in Israel and no information about it in Israel. Nobody knows why and what form and what is the price,” Levy said.
“One thing is clear. Israel is violating Syrian sovereignty and Israel is playing with fire with Iran. How long will the Syrians and the Iranians tolerate this?”
The regional tensions also come as violence has also escalated in Israel and the occupied Palestinian territories.
In the northern occupied West Bank, Israeli security forces on Saturday shot and killed a 20-year-old Palestinian, according to the Palestinian Health Ministry.
Ahed Salim, 20, was hit in the chest and stomach by live fire in Azzun near Qalqilyah, the ministry said.
Earlier in the day, four Palestinians were also wounded when Israeli settlers hurled stones at their cars at a checkpoint at the entrance to the city of el-Bireh.
The Wafa news agency reported additional Israeli settler attacks on Palestinian homes and vehicles in the town of Deir Ballout.
Israel has also been on edge after a car-ramming in Tel Aviv on Friday that killed an Italian man and wounded five other tourists. The Tel Aviv attack came hours after a Palestinian man shot and killed two Israeli sisters and wounded their mother near an illegal Israeli settlement in the occupied West Bank.
Amid the escalation, Israeli Defense Minister Yoav Gallant has extended a closure barring entrance to Israel for Palestinians from the occupied West Bank and Gaza Strip for the duration of Passover, while police beefed up forces in Jerusalem on the eve of sensitive religious celebrations.