"The Israel Defense Forces hit Hamas and the terrorist organization hard over the weekend. If attacks against Israeli civilians and the IDF continue, the response will be most harsh, " Israel Radio quoted Netanyahu saying at the start of the weekly cabinet meeting.
Later in the day, Netanyahu will convene the security cabinet to discuss the situation in the South, the radio said.
The prime minister's warning came amid reports of Hamas demands for a ceasefire, saying it is willing to abide by the truce if Israel halts all military action in Gaza, the radio said.
Despite this, on Sunday morning Palestinians fired a Grad missile and a Qassam rocket at Ashkelon and three mortar shells at the western Negev in southern Israel, the army said. No injuries were reported.
Defense Minister Ehud Barak told Israel Radio, Jerusalem is willing to accept a mutual ceasefire if Hamas stops firing rockets at Israel.
"If they stop firing on our communities, we will stop firing. If they stop firing in general, it will be quiet, it will be good," Barak told the radio.
Barak plans to seek approval for the purchase of additional Iron Dome anti-missile defense systems to be deployed in the south of the country, after the two batteries near Beersheba and Ashkelon intercepted 8 rockets fired at the cities during the weekend, Israel Radio said.
The United States is expected to approve the transfer of $205 million to purchase the batteries, The Jerusalem Post said, quoting a report on Army Radio.