The Code Red rocket alert sirens were triggered on the second night of Prince William's three-day visit to Israel.
"We are prepared for any scenario and our enemies would do well to understand this - now."
There were no casualties. In one of the settlements there were damaged buildings and vehicles.
Hamas attempted to justify its rocket attacks based on the IDF retaliation for Gaza's ongoing arson terror attacks.
The Code Red incoming rocket siren was triggered overnight repeatedlyTuesday after midnight.
Arab media reported the Izz a-Din al-Qassam military wing of Hamas claimed responsibility for Tuesday night's rocket fire at Israel.
Two rockets landed within Israeli territory. A third rocket didn't clear the border and landed within Gaza territory, according to the IDF.
Red Alert rocket sirens yanked Israeli families out of their beds at 4:40 am and again at around 5:15 am.
No physical injuries were reported -- albeit anxiety and sleep deprivation were common in most communities.
The air strikes were carried out in response to new rocket attacks launched by Gaza terrorists.
12:40 AM: Rocket Alerts begin sounding...
The video reveals the details of seven terror sites and the ordnance that was being produced and used by both of the Iranian-backed terrorist organizations in their effort to annihilate Israel.
"Residents of the Gaza Strip, it is time to wake up and understand that Hamas and Islamic Jihad are using you as hostages."
Mayor Uwe Becker posted his recommendation to social media on Tuesday towards the end of the first day of rocket and mortar attacks on southern Israel from Gaza.
"We must not drop the ball and we cannot lose sight of our main target -- Iran. The moment we destroy the head of the octopus, our situation ... will be much better."
"The Security Council should be outraged and respond to this latest bout of violence directed at innocent Israeli civilians."
According to the IDF, there were also a number of Red Alert sirens that were false alarms. The incidents were being investigated, the IDF said.
Gaza terrorists fired some 80 rockets and mortar shells at Israel on Tuesday, May 29.
"The IDF is prepared for a variety of scenarios and is determined to act against terrorist operatives and will continue to carry out its mission to protect the citizens of Israel."
A number of the traumatized residents were taken to a nearby hospital for medical care.
"The Municipal Hotline 106 is at your service for any question," Kiryat Gat authorities announced.
"Hamas has misappropriated billions of dollars of aid and bought missiles instead of food and built terror tunnels instead of schools and hospitals."
Tuesday marked the largest rocket and mortar attack against Israel from Gaza since 2014.
The actions of the terrorist factions Tuesday night and in the next 24 hours will determine whether Israel will be forced into a wartime stance, or simply that of a heightened alert.
Liberman: "Every place from which the terrorist organizations fire into Israeli territory is a legitimate target for the air force to attack, with all that entails."