Israeli Prime Minister Benjamin Netanyahu on Sunday said troops had responded "forcefully" to rocket fire from the Gaza Strip and could boost their response if a fragile truce announced on Saturday failed to hold.
"Regarding the situation in the south, the Israeli army acted forcefully against those who try to attack us and, if necessary, the army will act more forcefully still," Netanyahu warned at the start of a cabinet meeting.
"Our policy is to use force to restore security and calm to the residents of the south," he added.
Netanyahu spoke as a fragile second attempt at a truce between Israel and armed groups in Gaza appeared to be taking hold, with the military saying no rockets had been fired from the Palestinian territory since the ceasefire began at midnight on Saturday.
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An Israeli army spokeswoman said that by Saturday evening 28 rockets had slammed into southern Israel that day and on Friday, with another 10 brought down by the Iron Dome air defence system.
The current round of Israeli attacks and Palestinian retaliation began with air strikes on Monday morning, just hours after gunmen from Sinai carried out an ambush along Israel's southern border with Egypt, killing an Israeli civilian.
Israel has said its sudden spike in Gaza operations was "in no way related" to the Sinai border incident, with the military saying the air force was targeting militants poised to attack the Jewish state.
Since Monday, 15 Palestinians have been killed and several dozen others have been wounded, most of them militants, in multiple Israeli air strikes.
At least 152 rockets and mortar rounds have been fired into Israel from Gaza, wounding five Israelis including four border policemen.