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In another strategic move, Israeli forces seized a main highway in Gaza, slicing the territory in two.
Israeli forces detained 80 Palestinians — some of them suspected Hamas members — and transferred several to Israel for questioning, said military officials, speaking on condition of anonymity because they were not allowed to release the information.
The Gaza City area was rocked by shelling from both sides as gunboats in the sea and artillery and tanks closing in from the east unloaded thunderous fire.
After dark, the shelling reached deeper into residential areas. Fireballs lit up the horizon to the east, setting off blazes on the ground and silhouetting Gaza's tall buildings. Tracer fire ripped across the skyline.
The State Department said the U.S. was pressing for a cease-fire that would include a halt to rocket attacks and an arrangement for reopening crossing points on the border with Israel, said spokesman Sean McCormack. A third element would address the tunnels into Gaza from Egypt through which Hamas has smuggled materials and arms.
President George W. Bush emphasized "Israel's desire to protect itself."
"The situation now taking place in Gaza was caused by Hamas," he said.
The deputy head of Hamas' politburo in Syria, Moussa Abu Marzouk, rejected the U.S. proposal, telling the AP the U.S. plan seeks to impose "a de facto situation" and encourages Israel to continue its attacks on Gaza.
French President Nicolas Sarkozy, who unsuccessfully proposed a two-day truce last week, met with Palestinian President Mahmoud Abbas, who lost control of Gaza to Hamas in June 2007.
Europe "wants a cease-fire as quickly as possible," Sarkozy said after meeting Abbas, urging Israel to halt the offensive, while blaming Hamas for acting "irresponsibly and unpardonably."
A European Union delegation met with Israeli Foreign Minister Tzipi Livni.
"The EU insists on a cease-fire at the earliest possible moment," said Karel Schwarzenberg, the foreign minister of the Czech Republic, which took over the EU's presidency last week from France. Rocket attacks on Israel also must stop, Schwarzenberg told a news conference with Livni.
The EU brought no truce proposals of its own because the cease-fire "must be concluded by the involved parties," he added.
As the bruising campaign entered its 10th day Monday, Hamas pummeled southern Israel with more than 30 rockets and promised to wait for Israeli soldiers "in every street and every alleyway."