Israel's security cabinet on Sunday officially declared a state of war following Saturday's attacks by Hamas militants. The declaration allows "far-reaching military steps."
Israel was already carrying out strikes on buildings in Gaza.
On Saturday, Israeli Prime Minister Benjamin Netanyahu promised a harsh response to the militant attacks.
His office said the security cabinet had also approved steps to destroy "for many years" the military and governmental capabilities of Hamas and Islamic Jihad, the other militant group in the attacks.
It did not expand on what these steps would entail or say whether it would include a ground operation in Gaza.
Israel: 100 people abducted
More than 100 people have been kidnapped and 700 killed in Israel in large-scale attacks by the Islamist group Hamas, the Israeli government said on Facebook.
Hamas launched surprise attacks against Israel from Gaza on Saturday morning, while armed Palestinians simultaneously advanced into Israel by land, sea and air.
They took hostages in several Israeli towns and also abducted people in the Gaza Strip.
According to Israeli media reports, there are around 170 Israelis in captivity in the Gaza Strip.
Meanwhile, the Ministry of Health in Gaza said at least 370 people have died there so far as a result of Israeli retaliation. and around 2,200 were injured.