Israeli troops backed by air strikes fought to seize ground from Hamas militants deep inside the Gaza Strip on Monday despite international calls for a ceasefire in a conflict that has killed more than 540 Palestinians in 10 days. Israel's defense minister said the operation, aimed at stopping Hamas rocket attacks on southern Israel, could get more difficult before the mission was accomplished. Hamas vowed to fight on in “every street, every alley” and threatened to fire more rockets across the border into Israel. French President Nicolas Sarkozy, on a peace-brokering trip to the Middle East, and US President George W. Bush, in his final weeks in the White House, both appealed for a ceasefire. But disagreement on who should stop shooting first and on what terms made the chances of a pause soon remote. The death toll in Gaza rose to at least 541 people, many of them civilians. Among Monday's victims were 13 members of a Palestinian family killed in an Israeli strike on their home in a refugee camp, Palestinian medical officials said. Israeli soldiers and Islamist militants fought throughout the day and into the night on Monday. Militants fired mortars and grenades and detonated mines and tried to lure Israeli soldiers into built-up areas, witnesses said. Hamas said in a statement that its fighters had fired missiles at seven tanks in the same district and that 10 Israeli soldiers were killed. The Israeli army did not comment on the claim though it confirmed there was heavy fighting. Hamas reported at least one of its members was killed in the fighting. As night fell, Israeli troops were trying to capture a hill overlooking Jabaliya town and refugee camp and Hamas fighters were resisting them strongly, witnesses said. Heavy Israeli air and artillery strikes concentrated on that area. Israel's advances into Gaza have carved the 40 km (25 mile)-long coastal territory into two zones and forces have surrounded its largest urban area, Gaza City. Street fighting Hamas leaders rallied their combatants with defiant rhetoric. Thousands of fighters were waiting “in every street, every alley and at every house” to tackle them, Hamas military spokesman Abu Ubaida said in a broadcast speech. Hamas would increase its rocket strikes on Israel if the Israeli attacks on Gaza continued, Ubaida said. A rocket hit the Israeli port city of Ashdod, damaging a building and wounding two people, police said. Four Israelis have been killed by salvoes fired into Israel since the offensive began. In Ramallah, French President Sarkozy called for a ceasefire as soon as possible and said that “time is running against peace.” US President George W. Bush, speaking in Washington, blamed Hamas for provoking the bloodshed and said any ceasefire must include provisions to stop its rocket attacks. “Instead of caring about the people of Gaza, Hamas decided to use Gaza to use rockets to kill innocent Israelis,” he said. Truce On Monday Israel outlined three “fundamental principles” necessary for ending the military's air and ground offensive, according to a senior official. These include “substantially destroying” Hamas' military power and deterring Hamas from firing rockets against southern Israel. The third principle is creating a mechanism that will prevent Hamas from rearming through smuggling tunnels between Gaza and Egypt, the official said. International aid Germany pledged €11 million ($15.3 million) in aid to Gaza as part of its efforts to prevent the humanitarian situation in Gaza from deteriorating further. Exiled leader of Hamas, Moussa Abu Marzouk said Hamas was open to a truce but any agreement would have to include an end to the Gaza siege as well as an end to th blockade. He said any agreement which did not include these elements would “have no chance of suceeding.” Palestinian Foreign Minister Riyad Al-Malki said Arab countries were drafting a UN Security Council resolution demanding an end to the fighting.