"Israeli jets started to attack terrorist targets in the Gaza strip", the army said hours after a projectile hit the city of Beer Sheva.
The rocket fell into the garden of a house occupied by a family with three children who were being treated for shock, local media reported.
Lt. Col. Jonathan Conricus, a spokesman for the Israeli army, said at a press briefing that the rocket fired was a "midrange, locally produced rocket possessed only by two groups in Gaza, Hamas and Islamic Jihad".
"At the same time, we emphasize we are ready to confront the Israeli aggression".
The other rocket came down in the sea off Tel Aviv, 70 kilometres (45 miles) from Gaza, the army said.
Amid the spike in hostilities, a delegation led by Egyptian Intelligence Director Abbas Kamel that had been scheduled to arrive in Gaza on Thursday morning postponed the trip.
Netanyahu said that in a statement that unless attacks from Gaza ceased, "Israel will act with great force" to stop them.
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A member of Palestinian security forces loyal to Hamas inspects the scene of an Israeli air strike in the southern Gaza Strip October 17, 2018.
At least three other Palestinians were wounded in the strikes, the Gaza health ministry said.
Lieberman also ordered the the reduction of the permitted fishing zone along the Gaza coast to three nautical miles, the defence ministry body responsible for Palestinian civil affairs, COGAT, said.
Lieberman already suspended deliveries of fuel that had been trucked daily into Gaza under a deal brokered by the United Nations.
It had seen thousands of litres (gallons) of fuel paid for by gas-rich Gulf state Qatar delivered to boost power generation in the impoverished territory. "Extensive use has been made of lethal tactics such as throwing explosive charges and grenades at IDF soldiers, and there has been a rise in terror attacks caused by sending incendiary balloons and kites into Israel".
Nickolay Mladenov, the United Nations special coordinator for the Middle East peace process, called the developments "a risky escalation".
Another rocket from Gaza struck a beach near one of Israel's larger cities.
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Rivlin said there could be no easing of the blockade while Israelis remained under threat of rocket attack.
The groups also welcomed Egypt's effort "to fulfill the demands of the Palestinian people" and said they were prepared to "face any Israeli aggression".
Rivlin praised the fast reaction of Israelis in Beersheba, saying the mother's actions saved her family's lives.
Hamas clearly misinterpreted Israel's willingness to improve the humanitarian situation in Gaza and apparently thought it was the beginning of Israel's capitulation.
Gaza's two million residents endure dire living conditions including a shortage of safe drinking water and regular power cuts, partly because of the lack of fuel for the strip's power station.
Hamas has been ramping up the violent riots along the border fence in order to achieve the complete removal of what it calls the Israeli "blockade" or "siege". A war would be "devastating for the people of Gaza and for the Israelis who live across the border", he said.
A video footage was released, on Wednesday, showing an Israeli airstrike carried out in the northern besieged Gaza Strip, killing 25-year-old Naji Muhammad al-Zaanin.
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