Palestinian group Hamas launched the biggest surprise attack on Israel in years on Saturday, killing more than 20 people.
Fighters were sent across the border and a barrage of rockets were fired from the Gaza strip.
Israel's ambulance service reported at least 22 Israelis were killed in the attack so far with more than 250 wounded, but added that the toll was expected to rise.
Prime Minister Benjamin Netanyahu vowed to retaliate, saying "We are in a war and we will win it."
The Israeli military said it had launched air strikes into Gaza, where witnesses reported hearing heavy explosions, with at least two dead.
The attack marked one of the most serious escalations in the Israeli-Palestinian conflict in years.
Saudi Arabia says shrapnel from intercepted ballistic missile in Asir injures one
Israeli strike kills five in Gaza, health officials say
Nine injured in Australia as car crashes into crowd north of Sydney
India's 'cockroach' youth party to protest, demand poll chief's resignation
Congo's Ebola outbreak has killed more than 4,000, government data shows
