Jerusalem - Israeli forces began to close in on Gaza City Monday, ordering families in outlying towns and neighborhoods to flee, as world leaders launched a renewed push to bring the 10-day-old conflict to a swift end.

    So far, Israeli units have faced lighter-than-expected resistance from Palestinian militants in the second full day of a ground invasion that followed eight days of aerial bombardment intended to undermine the Gaza's control by the militant Islamic group Hamas. But civilian casualties are rising.

    Medical officials in the Hamas-controlled Gaza Strip said Monday that 523 Palestinians have been killed by Israeli attacks, including 111 children. That marks a dramatic spike from the early days of Israeli air strikes that primarily targeted Hamas-dominated police stations, government buildings, mosques the Israeli military said were being used to store weapons, and the homes of Hamas leaders.

    Early Monday morning, medical officials said, 11 members of one family, including five children, were killed in a northern Gaza City neighborhood after Israeli forces ordered them to leave their home.

    Family members said they sought safety in another apartment that was then hit by an Israeli strike.

    Civilian deaths are certain to rise as the Israeli forces move in on Gaza City's narrow streets and refugee camp alleys where Gaza militants have taken up positions.

    "Usually you have people trying to flee the area of conflict," said John Ging, the head of the United Nations refugee agency in the Gaza Strip. "But they don't have this choice in Gaza because they are trapped in a very, very densely-populated area."

    Palestinian militants continued to fire sporadic volleys of rockets and mortars into southern Israel on Monday, even as Israeli soldiers sought to seize areas of the Gaza Strip routinely used to fire rockets and mortars into southern Israel.

    Four Israeli civilians have been killed by Palestinian rocket attacks in the past 10 days.

    The military moves come as world leaders are making a new push to broker a cease-fire.

    French President Nicolas Sarkozy was expected to arrive in the Middle East on Monday evening for separate emergency meetings with Palestinian Authority President Mahmoud Abbas and Israeli Prime Minister Ehud Olmert.

    In parallel, a three-person European Union delegation met with Israeli leaders on Monday to call for an immediate cease fire.

    After talking with Israeli Foreign Minister Tzipi Livni, the delegation voiced its disagreement with the Israeli push to severely damage Hamas before the fighting ends.

    "The European Union insists on a cease-fire at the earliest possible moment," said Karel Schwarzenberg, the foreign minister for the Czech Republic, which became leader last week of the 27-member body. "We are not sharing the view that the cease-fire is only possible if all possible aims of the Israeli action are achieved."

    Israeli officials rebuffed an early attempt by Sarkozy to broker a 48-hour truce, but are now beginning to outline the parameters for ending the fighting.

    A senior Israeli official said the government was exploring ways to marginalize Hamas in any peace deal.

    Israel has three major objectives, said the official, who spoke on condition of anonymity because of the sensitive nature of the talks: Substantially curbing Palestinian rocket fire from Gaza, boosting Israel's image as a feared Middle East military power by severely damaging Hamas military capabilities, and ensuring that Palestinian militants are not able to continue rearming by using smuggler tunnels under the Gaza-Egypt border.

    While Israeli soldiers were preparing for a fierce fight, they have so-far faced lighter-than-expected resistance from Gaza militants. So far, only one Israeli soldier has been killed in the fighting.

    Some analysts suspect that Hamas fighters are trying to draw Israeli soldiers into the densely-populated urban areas where street-battles would be more difficult for the Israeli military.

    "Hamas's glorious fighters have disengaged from the IDF, leaving their bombs behind them as they fire mortar shells on the fly," Israeli columnist Ben Caspit wrote in Monday's Maariv newspaper, using the initials for Israel Defense Forces. "It turns out that there's a real difference between the ridiculous parades they put on in their camouflage uniforms and the dramatic shows of military prowess that get broadcast on TV and the real thing."

    But Caspit warned that a tougher fight may still be ahead.

    "True, Israel overestimated Hamas's strength and capabilities, but we mustn't now fall into the trap of underestimating them," he wrote. "All of the explosives that were packed into the rockets that were fired at Israel could be fit into just two bombs that the IAF (Israel Air Force) dropped on them. And the IAF has already dropped a thousand such bombs on them."