At least three Palestinians were killed by Israeli air strikes on the Gaza Strip and an Israeli civilian died in a barrage of rocket fire in the worst violence between the two sides since the 2014 war.
The latest escalation came less than 24 hours after at least seven Palestinians were killed in a covert Israeli operation in the besieged enclave.
Hamas, the group administering the Strip, said one of Monday's air attacks destroyed the building of its television station. There was no immediate word of casualties.
Along with the air raids, Israeli artillery units also shelled positions across the densely populated enclave.
The moment when Israeli warplanes bombing the building of Al-Aqsa TV.
Israel said its Iron Dome system intercepted many of the 300 missiles fired from the Palestinians. One, however, hit a bus and another struck a building in southern Israel.
One Israeli man was pulled out dead from the ruins of the building hit by rockets, the emergency service said on Tuesday. A woman, also recovered from the debris in Ashkelon, was in a critical state, said the organisation United Hatzalah.
One soldier was seriously wounded, the Israeli army said, and at least 27 other Israelis were also hurt in the projectile fire from Gaza.
UN Secretary-General Antonio Guterres pressed all sides to back down. "He urges all parties to exercise maximum restraint," UN spokesman Farhan Haq said.
UN Special Coordinator Nickolay Mladenov was working closely with Egypt and all concerned parties to restore calm, Haq said in a statement.