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.
Israeli strikes kill two in Gaza, destroy medicine storage warehouses
Thirteen die in tourist plane crash over Peru's Nazca Lines
Restaurant explosion in central Moscow kills three, injures 15
All 10 climbers confirmed killed in Pakistan avalanche
