Israeli tanks and helicopter gunships went blazing into towns across the Gaza Strip on Tuesday attacking Hamas targets and searching for its leaders as the war death toll passed 580.
Troops fought Islamist militants around the back alleys of Gaza's main city in the heaviest fighting of the 11-day-old offensive to halt Hamas rocket attacks on Israel.
On the diplomatic front, Arab nations pressed the case for a UN Security Council resolution condemning Israel's action but the Jewish state rejected ceasefire calls by French President Nicolas Sarkozy and other leaders.
"Europe must open its eyes," President Shimon Peres told an EU ministerial delegation that demanded a truce. "We are not in the business of public relations or improving our image. We are fighting against terror and we have every right to defend our citizens."
Black smoke covered the districts of Gaza City and the edges of Deir al-Balah and al-Bureij where heavy fighting raged on Tuesday.
Israeli tanks backed by helicopter gunships also rolled into the southern town of Khan Yunis before dawn, to be met by return fire from Hamas and its allies, witnesses said.
Israeli strikes hit two UN-run schools, one crowded with refugees, killing at least five Palestinians, medics and UN officials said.
Two people were killed when an artillery shell slammed into a school in Khan Yunis and three people were killed in an air strike on a school in the Shati refugee camp in Gaza City, they said.
In the face of the Israeli assault, about 12 Hamas rockets were fired over the border, one reaching 45km inside Israeli territory, the deepest yet, lightly wounding a baby, the army said.
Three civilians and one soldier have been killed by rocket fire inside Israel since the offensive was launched.
Protests against Israel's action have spiralled around the globe and French President Nicolas Sarkozy led new calls for a truce in talks with Israeli and Palestinian leaders on Monday.
"We, Europe, want a ceasefire as soon as possible," Sarkozy said in Jerusalem. "Time is working against peace. The weapons must be silenced and there must be a temporary humanitarian truce."
But Israeli Prime Minister Ehud Olmert vowed that the campaign would continue until Israel completely wiped out Hamas's ability to fire rockets into Israel.
Sarkozy also called Hamas rocket attacks "irresponsible and unforgivable," sparking the Islamists' retort that he was "totally biased" towards Israel.
Israel launched Operation Cast Lead on Hamas on December 27 with a massive air bombardment of Gaza, and sent in thousands of ground troops a week later.
Since then, at least 582 Palestinians have been killed, including 159 children, and more than 2,700 wounded, according to Gaza medics.
The International Committee of the Red Cross said people were dying because ambulances could not reach them amid the fighting.
Four Israeli soldiers were killed in two friendly fire incidents during the overnight surge in fighting, the army said. Five have now been killed since Saturday.
Olmert and Sarkozy agreed the French leader should pursue a peace deal involving Egypt which brokered a six-month truce that ended on December 19. Hamas refused to renew the deal, sparking the war.
The UN Security Council was to meet again on Tuesday to weigh an Arab call for an immediate ceasefire and for protection of Palestinian civilians, diplomats said.
Israel's main ally the United States has given strong support to the operation, with President George W Bush saying any truce must ensure an end to rocket fire.
"I understand Israel's desire to protect itself and that the situation now taking place in Gaza was caused by Hamas," he said.
The fighting in one of the world's most densely populated places where minors make up a large chunk of the 1.5 million population has taken a huge civilian toll, particularly among children.
There are no power or water supplies in the territory and finding food is a daily struggle.
Israeli officials have insisted they are doing all to prevent civilian casualties and have blamed Hamas for operating from civilian centres.
Hamas, which has ruled Gaza since seizing the coastal enclave in June 2007 from forces loyal to Abbas, has remained defiant.
"Victory is coming," its senior leader in Gaza, Mahmud Zahar, said in a television broadcast.
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