Prime Minister Benjamin Netanyahu instructed the Israel Defense Forces to "continue with its forceful attack against terrorists in the Gaza Strip" following the barrage of rockets on Israel over the weekend.
Netanyahu, who spoke at the start of the weekly cabinet meeting, announced that the IDF would increase its presence along the Gaza border by adding more artillery and infantry troops. "Hamas is responsible not just for its own attacks, but those of the Palestinian Islamic Jihad, and it is paying a heavy price for that," Netanyahu said.
A rocket fired from Gaza killed an Israeli civilian on Sunday and two Palestinian terrorists were killed in an Israeli strike as cross-border hostilities ran into their third day.
Air-raid sirens sent Israelis in the country's south running to their shelters through the night as interceptor missiles blew up rockets in the sky. Israel Police said one of the rockets launched from Gaza hit a house in the city of Ashkelon, killing one man.

The 58-year-old man, identified as Moshe Agadi, was a father of four. His brother told the Israeli media that he was outside his home smoking when the sirens blasted and did not have time to take cover. "They tried to save him on the way to the hospital, but he did not survive," his bother told Reshet Bet radio.
Israeli bombings in Gaza shook buildings and resulted in several terrorists killed. The Palestinian Islamic Jihad terrorist group said two of its men were killed in an Israeli raid before dawn.
Egyptian and U.N. mediators, credited with brokering cease-fires in previous rounds of violence, were working to prevent further hostilities.
The latest round of violence began on Friday when a Palestinian Islamic Jihad (PIJ) sniper fired at Israeli troops, wounding two soldiers. Israel retaliated with an airstrike that killed two terrorists from the Islamist group Hamas, which controls Gaza.

Two other Palestinians who tried to target Israeli soldiers near the border fence were killed by Israeli forces on the same day, Palestinian officials said.
Since Saturday, Hamas and Islamic Jihad fired more than 400 rockets at Israeli villages and cities, the military said, and Israel hit back with tank shelling and airstrikes at some 200 targets in Gaza.
Video: Reuters
Islamic Jihad said in a statement that the rocket barrages were a response to Friday's events and that Israel was delaying the implementation of previous understandings brokered by Cairo.
Israeli military spokesman Lt. Col. Jonathan Conricus said on Saturday that Israel was prepared to intensify attacks. He added that PIJ was trying to destabilize the border and blamed Hamas for failing to rein it in.
In a joint statement on Saturday, Hamas and Islamic Jihad said: "Our response will be broader and more painful if the enemy pursues its aggression."

The escalation comes just ahead of both the Muslim holy month of Ramadan and Israel's Independence Day holiday.
Israel is due to host the 2019 Eurovision Song Contest in less than two weeks in Tel Aviv, toward which long-range rockets were launched in mid-March.
Although aerial exchanges are frequent, Israel and Hamas have managed to avert all-out war for the past five years.