Israel on Friday suspended fuel deliveries to the Gaza Strip, after fresh protests along the border that saw seven Palestinians killed by Israeli troops.
The protests intensified as Egyptian-mediated cease-fire efforts faltered.
Israel also closed both its border crossings with Gaza in reprisal, further isolating the blockaded enclave where deteriorating living conditions have stoked violent protests along the border.
Israel's military began targeting militant sites in Gaza on Wednesday, calling the attacks a response to earlier rockets that were launched from Gaza, one of which struck a residential home in southern Israel.
The family of three children narrowly escaped injury after their mother moved them into the safe room, with much of the rest of the house destroyed, the army said.
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".
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"At the same time, we emphasize we are ready to confront the Israeli aggression". - The border protests since March 30 have been labelled the "Great March of Return" because they call for Palestinian refugees to return to their former homes inside what is now Israel.
Hamas and other Gaza militant groups denied firing the rocket.
The IDF later said the infiltration attempt was meant to kidnap a number of IDF soldiers after which Hamas would demand a complete removal of the embargo on goods it uses to produce weapons, missiles and terror tunnels.
Residents in Gaza said the aircraft targeted three locations, but there were no initial reports of casualties. Five other Palestinians were wounded in separate attacks.
"That's the only way to lower the level of violence to zero or close to zero", Israeli newspaper Haaretz reported Defence Minister Avigdor Lieberman as saying on Tuesday, after Israeli forces shot at a group of Palestinians allegedly trying to send incendiary balloons into Israeli neighbourhoods near Gaza that morning.
It also reduced the permitted fishing zone along the Gaza coast to three nautical miles.
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Growing voices within Israel's leadership have been calling for a stronger response to ongoing weekly protests along the Gaza border fence.
During a meeting with Israeli President Reuven Rivlin on Wednesday, UN envoy Nickolay Mladenov called the latest rocket launches a "dangerous escalation".
Another rocket from Gaza struck a beach near one of Israel's larger cities. "Majority turned back into Gaza, but three of them continued to move on toward a military outpost, where they were shot and killed".
Cairo has been holding talks with Hamas on a truce with Israel and ways to end 11 years of division with Palestinian President Mahmoud Abbas's Fatah faction in the occupied West Bank.
Its two million residents endure routine power cuts and a chronic shortage of safe drinking water, and more than two-thirds are dependent on worldwide aid.
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