By Nidal al-Mughrabi
GAZA (Reuters) - Israel's offensive in the Gaza Strip killed more than 30 Palestinian civilians on Tuesday, medical officials said, and international efforts to secure a ceasefire focused on an Israeli demand to prevent Hamas from rearming.
"That is the make-or-break issue," Mark Regev, a spokesman for Israeli Prime Minister Ehud Olmert, said about ensuring an end to weapons smuggling along the Gaza-Egypt frontier.
A senior Israeli official said French President Nicolas Sarkozy, on a Middle East visit and in partnership with Egypt, was pursuing "a serious initiative" for a ceasefire in Israel's 11-day-old operation and Hamas rocket attacks on Israeli towns.
Talks were focusing, the official said, on the size of an "international presence" along the blockaded Gaza-Egypt border, where rockets and other weapons have reached Hamas through a network of tunnels.
Tony Blair, the Middle East envoy of major powers sponsoring Israeli-Palestinian peace talks, said Sarkozy, the European Union and the United States were all in agreement that new anti-smuggling measures would be needed to clinch a ceasefire.
"What is being talked about is a credible plan to stop the smuggling," Blair, a former British prime minister, told reporters in Jerusalem.
He said he hoped the plan could be completed quickly and that enhanced Israeli security would lead to "a significant advance in opening up Gaza to the outside world."
In Damascus, Sarkozy, who met Olmert and Palestinian President Mahmoud Abbas on Monday, said after talks with President Bashar al-Assad he had no doubt the Syrian leader "will throw all his weight to convince every one to return to reason."
Syria is one of the main backers of Hamas, an Islamist group that seized the Gaza Strip from Abbas's Fatah group in fighting in 2007.
Hamas, which has rebuffed Western demands to recognise Israel, end violence and accept existing interim peace deals, has demanded a lifting of the blockade of the Gaza Strip in any future ceasefire.
CIVILIAN DEATHTOLL RISES
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.
Palestinian medical officials said 35 Palestinian civilians were killed on Tuesday, including 11 in a house that was bombed from the air, 10 on a beach hit by naval shells and three people who had taken refuge in a U.N.-run school.
Four militants also were killed, medical officials said.
Deaths recorded by Palestinian medics reached 588.
Most of the several dozen deaths reported by hospitals in the Hamas-run Gaza Strip in recent days have been civilians.
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.
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.
Nine Israelis, including three civilians hit in Palestinian rocket attacks, have been killed in the conflict.
There was intense fighting overnight on the outskirts of the city of Gaza, where some residents huddled indoors in fear and others fled.
Hearing Israeli tanks approaching, Rami Mohammad-Ali and his wife gathered up their three children and ran out of their home in a Gaza suburb for the precarious safety of his brother's house deeper inside the city.
"I didn't even bother to close the door. The lives of my children were more important. Their tears poured on my cheeks as I held them and ran," he said.
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.
In a "friendly fire" incident, an Israeli tank shell killed three Israeli soldiers and wounded 24 other troops on Monday.
The Israeli casualties -- the highest since Israel launched "Operation Cast Lead" -- raised questions in the Jewish state over whether its leaders should press on with the offensive.
"This time, we cast lead on ourselves," said a commentator on Israeli Army Radio.
An Israeli officer was killed in a separate incident, apparently also by Israeli fire, the army said.
Israel launched the current offensive after Hamas called off a six-month truce last month and stepped up cross-border rocket attacks in what it called a response to Israeli raids and a blockade of the Gaza Strip.
Heavy Israeli casualties in the Gaza fighting could erode strong public support for the operation and affect the outcome of Israel's February 10 national election.
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)