Airstrikes were conducted on the northern Gaza town of Beit Lahiya in response to three mortar shells fired at the western Negev Tuesday, Haaretz reported.
Two shells fired Wednesday exploded in an open field near Sderot, officials said.
The events Tuesday were the latest violation of the understandings that followed Israel's Operation Pillar of Defense, an eight-day campaign to stem rocket fire from the strip, Israeli officials said.
"We hold Hamas responsible for everything fired from the Gaza Strip into Israel," Israeli Defense Minister Moshe Ya'alon said Wednesday. "We will under no circumstances tolerate a routine trickling in of fire on our citizens or our forces."
In February, a rocket was fired at Ashkelon but caused no damage or casualties. In early March, a bullet fired from Gaza hit the windshield of the vehicle carrying the commander of the Israeli military's Northern Gaza Territorial Brigade. Four rockets were fired into Israel during U.S President Barack Obama's visit two weeks ago.
Hours after Ya'alon visited the Golan Heights Tuesday, a mortar shell and gunfire from Syria struck two areas where Israeli troops were patrolling, Haaretz said. Israeli tanks fired shells in response.
While he was touring the area, Ya'alon said Israel wouldn't intervene in the Syrian civil war but would respond to violations of its security interests.
"Across the border a bloody civil war has been taking place for the past two years with tens of thousands dead but we will not intervene as long as the fighting does not affect our security interests," Ya'alon said. "When it does, whether the sporadic shooting is intentional or not, we will respond ... ."