The report cited the Al-Quds Brigades, a different militia from the armed wing of the larger Palestinian Islamic Jihad with a similar name, and said it fired rockets in response to a police attack on the Al-Aqsa Mosque.
In Syria, an adviser to President Bashar al-Assad described the rocket attacks as part of a previous, current and ongoing response to a brutal enemy.
Israeli security forces in the occupied West Bank shot dead a 20-year-old Palestinian in the town of Azun, sparking protests in the area, Palestinian health officials said.
His death comes at a time of unprecedented violence in the West Bank.
At least 19 people have been killed so far in Palestinian attacks on Israelis – including the shooting death of two British Israelis near a settlement in the Jordan Valley on Friday, and an Italian man killed in a collision with a suspect car in Tel Aviv. The tourist was killed.
The rocket fire from Syria came against a backdrop of heightened Israeli-Palestinian tensions triggered by an Israeli police raid on Jerusalem's most sensitive site, the holy compound home to the Al-Aqsa Mosque.