Israel launched air strikes on Gaza late Wednesday after dozens of rockets were fired from the enclave into its territory, with injuries reported on both sides.
Smoke plumes could be seen rising from Gaza City following the military's announcement it was targeting "terror sites in the Gaza Strip".
At least two Palestinians were wounded in raids aimed targeting a Hamas base in the southern Gaza Strip, the enclave's health ministry said.
The strikes came after two rockets launched from the coastal enclave hit the town of Sderot, near Gaza's northern border, police and the army said.
One person was lightly wounded by shrapnel while several others were treated for shock in Sderot, the United Hatzalah medical service said.
Sirens were sounded in several areas close to the border with Gaza, warning residents to seek immediate shelter, the Israeli army said.
"As of now, 36 rocket launches were identified from Gaza towards Israel," the army wrote on Twitter.
The majority hit open areas while four were intercepted, it said.
Israel says it holds Hamas responsible for all fire coming from the long-blockaded coastal territory.
Israeli television broadcast images of a house and cars reportedly damaged by the rockets in Sderot.
Parts of the town have been closed off and police bomb disposal units were at the scene of the strikes, a spokesman for the force said.
The strikes came after two fighters from the military wing of Hamas, which rules Gaza, were killed by Israeli fire on Tuesday.
Hamas warned Israel -- with which it has fought three wars since 2008 -- it would pay for the attack.
The escalation comes after the Hamas leadership convened for a rare meeting in Gaza on Friday.
The gathering had raised hopes a deal for a lasting truce with Israel, with the backing of Egypt and the United Nations.
Clashes along the Gaza border since the end of March have seen at least 160 Palestinians killed by Israeli fire.
One Israeli soldier has been shot dead by a Palestinian sniper.