Thousands of rockets have been fired into Israel from the Gaza Strip in a surprise attack by the Hamas militant group on Saturday morning.
Large plumes of black smoke could be seen rising from a number of Israeli towns.
Israel's defence minister said Hamas had "launched a war" and its troops were "fighting against the enemy at every location".
Israeli Prime Minister Benjamin Netanyahu said in a statement: "We are at war and we will win."
Mr Netanyahu added: "Our enemy will pay a price the type of which it has never known."
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Social media images showed cars on fire and damaged buildings, and the Israeli ambulance service reported one woman had been killed and at least 15 others wounded.
Phone footage also showed Hamas fighters attempting to reach Israel on small boats, and in a highly unusual development, a number of fighters appeared to have crossed the border using paragliders, reaching the town of Sderot