The strikes came after four soldiers were injured, two seriously, after an improvised explosive device detonated near them on the southern border of the Gaza Strip.
Later on Saturday rockets were fired from Gaza, one which hit a home in southern Israel.
But he insisted that "from our point of view Hamas is responsible" and said the explosive had been planted during a protest arranged by the group on Friday.
Israeli radio channel Reshet Bet reported that a Palestinian source claimed that Hamas leaders informed Egypt that they are not interested in escelating the current conflict with Israel and that they are not those responsible for the attack on IDF soldiers on Saturday.
Police said the third had rocket hit a structure in a community near Gaza, causing damage but no casualties.
In mid-December, Israeli Defense Minister Avigdor Lieberman said Tel Aviv would no longer play "ping-pong" by exchanging rocket attacks with the Palestinian militants.
In response, Hamas's military wing, Izz ad Din al Qassam, claimed that it had used anti-aircraft missiles against Israeli jets flying over the coastal territory.
Israeli fighter jets attacked terrorist targets in Gaza overnight Saturday, in response to recent terrorist attacks, the IDF Spokesperson's Unit said in a statement. The Hamas-run health ministry said at least two people were wounded.
It was one of the most serious incidents on the border of the Hamas-ruled blockaded enclave since the Islamist movement and Israel fought a war in 2014.
The Israeli army responds automatically to any strikes on its territory, generally targeting Hamas facilities.
Israeli media said it was the highest number of Israelis wounded in a single incident since the 2014 Gaza war.