In Washington, State Department spokesman Sean McCormack said the US would like an immediate ceasefire but one that is sustainable and not time-limited — comments that stopped short of a formal demand for a truce now. International efforts are under way to end the fighting have focused on securing a deal that would meet Israel’s demand that Hamas, an Islamist group in charge of the Gaza Strip, could not rearm once hostilities end. “If there is an end to terror, an end to the smuggling of ammunition from Sinai to Gaza, the Israeli fighting will stop,” Israeli Prime Minister Ehud Olmert said, referring to rockets and other weaponry Hamas obtains through tunnels under the Gaza-Egypt border.

In fighting on Tuesday, Israeli forces pushed into the southern town of Khan Younis and battled Hamas militants on the outskirts of the city of Gaza. Palestinian medical officials said four militants were killed. According to the Palestinian Health Ministry in the Gaza Strip, at least 631 Palestinians have been killed and more than 2,700 wounded since Israel began its offensive.

Ten Israelis, including three civilians hit by rocket fire, have been killed in the conflict. At least five rockets landed in Israel on Tuesday, including one that hit the town of Gadera, 28 km (17 miles) from Tel Aviv. A three-year-old girl was wounded.

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. Commenting on the deaths at Jabalya school, Sarkozy said during a visit to French UN peacekeepers in south Lebanon: “It reinforces my determination for all this to stop as quickly as possible. Time is working against us. We must find a solution.”