By Nidal al-Mughrabi
GAZA (Reuters) - Israel moved forces into a southern Gaza town on Tuesday and demanded Hamas be prevented from rearming as a main condition for a ceasefire in an 11-day-old conflict in which hundreds of Palestinians have been killed.
While international truce efforts gathered speed after the New Year's holiday, an Israeli air strike killed three Palestinians in a U.N. school in the Gaza Strip where people had sought refuge from the fighting, medical officials said.
An Israeli tank shell killed three Israeli soldiers and wounded 24 other troops on Monday, in "friendly fire" that raised questions in the Jewish state over whether its leaders should press on with the crushing offensive.
An Israeli officer was killed in a separate incident, apparently also by Israeli fire, the army said.
Palestinian witnesses said Israeli forces pushed into Khan Younis in southern Gaza as the army widened the ground assault it launched four days ago against Hamas militants after a week of air strikes failed to stamp out cross-border rocket fire.
There was intense fighting overnight on the outskirts of the city of Gaza, where residents huddled indoors in fear. Deaths recorded by Palestinian medics reached 564.
Most of the several dozen deaths reported by hospitals in the Hamas-run Gaza Strip in recent days have been civilians.
The Israeli military said it killed 130 militants since Saturday, a figure that suggested the total Palestinian death toll since December 27 might be close to 700 and that bodies could still be on the battlefield.
Many of the Gaza Strip's 1.5 million people lack food, water or power. In southern Israel, schools remained closed and hundreds of thousands of people have been rushing to shelter at the sound of alarms heralding incoming rockets.
Palestinian medics, reporting on casualties before the deaths at the U.N. school, said 20 Palestinian civilians were killed on Tuesday, including 10 people who were hit by naval shells along the beach in the central Gaza Strip. Two militants were also killed in fighting.
Nine Israelis, including three civilians hit in Palestinian rocket attacks, have been killed in the conflict.
At least five rockets fired from the Gaza Strip landed in Israel on Tuesday, including one that hit the town of Gadera, 28 km (17 miles) from Tel Aviv, police said. A three-year-old girl was wounded.
A spokesman for Prime Minister Ehud Olmert, spelling out a crucial condition for a ceasefire, said Israel would not agree to a truce unless it included provisions to prevent Hamas from rearming.
"That is the make-or-break issue," said the spokesman, Mark Regev.
Regev said that was Olmert's message in talks on Monday with French President Nicolas Sarkozy, who called in meetings with Israeli and Palestinians leaders for a rapid Gaza ceasefire.
Regev said Hamas, which seized the Gaza Strip from the rival Fatah group in 2007 and has smuggled in weapons through tunnels running under the border with Egypt, used the previous six-month ceasefire brokered by Cairo to double the range of its rockets from 20 km (12 km) to 40 km (24 miles).
Hamas has demanded a lifting of Israel's blockade of Gaza in any future ceasefire.
Israel's military, describing Monday's shelling of an Israeli force by an Israeli tank, said soldiers from the Golani infantry brigade were hit while occupying a building in the northern Gaza Strip.
The brigade's commander, a colonel, was among the wounded.
The incident caused the military's highest casualty toll since Israel launched its "Operation Cast Lead" offensive against Hamas.
"This time, we cast lead on ourselves," said a commentator on Israeli Army Radio, who in an interview with a senior Defence Ministry official questioned whether the operation was achieving its declared goal of halting Hamas rockets, noting there has been little let-up in cross-border fire on Israeli towns.
Columnist Amos Harel, writing in Israel's Haaretz newspaper, said the death of the three soldiers from the crack Golani infantry brigade was "a significant first achievement" from Hamas's perspective.
"For the first time, Israeli TV broadcasts raised the question of whether it was worthwhile for the operation to continue," Harel wrote.
Israel launched the current offensive after Hamas called off a six-month truce last month and stepped up cross-border rocket attacks in response to Israeli raids and a blockade of the Gaza Strip.
Israel, whose leaders fight a parliamentary poll on February 10, made clear its priority was securing the safety of its citizens. But heavy Israeli casualties could erode strong public support for the operation.
Israel pulled its troops and more than 8,000 settlers out of Gaza in 2005 after 38 years of occupation in a move that many at the time hoped would lead to a breakthrough for relations between Israel and the Palestinians.
(Additional reporting by Adam Entous in Jerusalem, Writing by Jeffrey Heller and Alastair Macdonald, Editing by Samia Nakhoul)