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But Rice added that any solution must address Israel's security.
"There must be a solution this time that does not allow Hamas to use Gaza as a launching pad against Israeli cities. It has to be a solution that does not allow the rearmament of Hamas, and it must be a solution that finds a way to open (border) crossings so that Palestinians in Gaza can have a normal life," she said.
In the wake of the criticism over civilian casualties, Israel agreed to set up a "humanitarian corridor" to ship vital supplies into the Gaza Strip. Under the plan, put forward by the Israeli Defense Ministry, Israel would suspend attacks in certain areas to allow people to get supplies.
At U.N. headquarters, Secretary-General Ban Ki-moon called the Israeli bombardment of U.N. facilities in Gaza "totally unacceptable." Israel's shells have fallen around three schools, including the girls school hit Tuesday, and a health center for Palestinian refugees.
Ban added that it was "equally unacceptable" for militants to take actions that endanger Palestinian civilians, referring to the practice of militants making attacks from residential areas.
Some 15,000 Palestinians have packed the U.N.'s 23 Gaza schools because their homes were destroyed or to flee the violence. The U.N. provided the Israeli military with GPS coordinates for all of them.
The three mortar shells that crashed down on the perimeter of the U.N. school struck at midafternoon, when many people in the densely populated camp were outside getting some fresh air, thinking an area around a school was safe.
Images recorded by a cameraman from AP Television News showed crowds fleeing the scene, pavements smeared with blood and battered bodies being carried off by medics and bystanders. A youth who limped away was helped along by several others. Sandals lay scattered on the pavement by a pock-marked wall.
"There's nowhere safe in Gaza. Everyone here is terrorized and traumatized," said John Ging, head of Gaza operations for the United Nations Relief and Works Agency.
An Israeli military statement said it received intelligence that the dead at the girls school included Hamas operatives, among them members of a rocket-launching squad. It identified two of them as Imad Abu Askar and Hassan Abu Askar.