Israeli Prime Minister Benjamin Netanyahu said on Thursday that Gaza rulers Hamas were responsible for any attacks from the Palestinian enclave, after deaths on both sides.
"We have recently been subject to attacks against us," he said at a pilots' graduation ceremony at the Hatzerim air force base in southern Israel.
"Israel holds Hamas responsible for all the attacks launched on us. We will strike at those who attack us, and at those who support them," he said in remarks that were also broadcast on radio.
Confrontations between the sides peaked on Tuesday, when a sniper inside the Gaza Strip killed an Israeli fixing the border fence.
Israel retaliated against "terror sites" in Gaza using warplanes and tanks, killing a toddler and wounding at least six people.
The sniper attack has been attributed to a small Palestinian faction unrelated to the Islamist Hamas.
An ensuing tense quiet has held, despite Palestinians in Gaza firing a projectile that hit an uninhabited area in southern Israel early on Thursday.
A military spokeswoman told AFP it caused no damage or injuries.
Speaking at the same air force ceremony, Defence Minister Moshe Yaalon said Israel would not accept the "trickle of terror from the Gaza Strip, where Hamas is sovereign".