A Palestinian looks from a window at the rubble of a house destroyed in an Israeli airstrike in... 
(AP)
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Israeli Defense Minister Ehud Barak said the offensive would go on until Israel achieved "peace and tranquility" for residents of southern Israel.
One of the rockets struck a large outdoor market that was closed at the time in the town of Sderot, just across Gaza's northeastern border. Another hit a kindergarten in the coastal city of Ashdod, north of the strip. The kindergarten, like schools across southern Israel, was closed and empty because of the rocket threat.
Israel has three main demands: an end to Palestinian attacks, international supervision of any truce, and a halt to Hamas rearming. Hamas demands an end to Israeli attacks and the opening of border crossings to vital cargo.
Livni said the operation was designed to change the rules of Israel's struggle against Hamas after years of firing rockets at Israel. From now on, she said, "when Israel is targeted, Israel is going to retaliate."
Israeli military spokeswoman Maj. Avital Leibovich said Hamas was to blame for civilian casualties because it operates in densely populated areas.
"If Hamas chose cynically to use those civilians as human shields, then Hamas should be accountable," she said.
Hamas leader Mahmoud Zahar exhorted Palestinians to fight the Israeli forces and target Israeli civilians and Jews abroad.
"The Zionists have legitimized the killing of their children by killing our children. They have legitimized the killing of their people all over the world by killing our people," Zahar said in a grainy video broadcast on Hamas TV.
Israel's operation has sparked anger across the Arab world and has drawn criticism from countries such as Turkey, Egypt and Jordan, which have ties with Israel and have been intimately involved in Mideast peacemaking.
In Beirut, Lebanon, protesters tried to pull away barbed wire blocking their path to the U.S. Embassy. They were driven back with heavy blasts of water.
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Barzak reported from Gaza City, Keyser from Jerusalem.
Copyright 2009 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.
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