GAZA CITY (AFP) - Israeli troops battled Hamas fighters in Gaza's main city for the first time Monday - after dozens died in a day of clashes - while the government fended off worldwide calls for a ceasefire. Amid raging combat in Gaza City, and as the Palestinian death toll rose to 555, French and Russian presidents Nicolas Sarkozy and Dmitry Medvedev both demanded a halt to the conflict. But Israeli ministers said the offensive would go on. Large explosions and heavy exchanges of fire rocked the Shejaiya neighbourhood of eastern Gaza City as Israel pressed its campaign to halt Hamas rocket attacks. Hamas said in a statement that its fighters had fired missiles at seven tanks in the same district. The group's armed wing said that ten Israeli soldiers were killed in the clashes. The Islamic Jihad movement said several of its members were killed in the fighting. Israeli military sources confirmed that troops were involved in heavy clashes in that area, but refused to comment whether its forces had suffered casualties. Flares lit up the skies over the blacked-out neighbourhood. Assault helicopters were also seen. At least 12 children were among 50 new bodies taken to Gaza hospitals after air missile and tank attacks Monday, medics said. But as Israel intensified its air and ground operation, Foreign Minister Tzipi Livni rejected EU calls for an immediate ceasefire, saying Israel was aiming to change the "equation in this region." "We are fighting with terror and we are not reaching an agreement with terror," Livni declared after talks with an EU ministerial delegation led by Czech Foreign Minister Karel Schwarzenberg. Israel acted to change a situation where "Hamas targets Israel whenever it likes and Israel shows restraint," she said. "This is no longer going to be the equation in this region. When Israel is being targeted, Israel is going to retaliate." Livni said Israel would keep on battling Hamas. Schwarzenberg, whose country currently holds the rotating EU Presidency, repeated the bloc's call for an immediate halt to Israel's military offensive in Gaza. "We presented the Israeli foreign minister with the view of the European Union that a ceasefire should be established as soon as possible as that rockets have to stop," Karel Schwarzenberg told reporters in the joint media conference. After a meeting in Ramallah with the Palestinian Authority leader, Sarkozy said he would tell Israeli leaders that "the violence must halt". The French president called the Hamas rocket attacks on Israel "irresponsible and unforgiveable". Russian President Dmitry Medvedev called for an immediate ceasefire after telephone talks with Abbas earlier, the Kremlin said. But US President George W Bush said any Gaza ceasefire must ensure Hamas militants can no longer fire rockets on Israeli towns. "I understand Israel's desire to protect itself and that the situation now taking place in Gaza was caused by Hamas," Bush said. Fighter jets carried out more than 30 airstrikes during the day. The military said they hit a mosque "where arms were being stored, as well as houses containing arms caches and vehicles that were transporting rocket launchers and armed men." Naval ships off the coast also bombarded targets to help the ground offensive launched on Saturday night. The Israeli strikes killed 50 Palestinians on Monday, including 12 children, medics said. A couple and their five children were killed by one navy shell, medics said. Three children were killed by a tank shell in Zeitun in the Gaza City suburbs and two were killed in Shati by a naval strike, they said. At least 555 Palestinians - including almost 100 children - have been killed since Israel launched Operation Cast Lead on December 27, Gaza's emergency services said. More than 2,700 have been wounded. Israel says dozens of Hamas fighters have been killed while one Israeli soldier has been reported dead and 55 wounded since Saturday. Defence Minister Ehud Barak told parliament the Hamas war would go on. "Gaza City is partially surrounded," Barak told MPs. "We have hit Hamas hard, but we have not yet reached all the goals that we have set for ourselves and the operation continues." Three civilians and one soldier have been killed by rockets fired from Gaza since Israel's operation started. More than 30 rocket and missile attacks were reported on Monday. One hit a kindergarten which was closed because of the crisis. Mauritania, one of only three Arab countries to have full diplomatic ties with Israel, withdrew its ambassador in protest. Israeli forces consolidated their hold on parts of Gaza Strip, seizing three high-rise buildings on the outskirts of the territory's biggest city and killing seven children as Hamas activists pummelled southern Israel with rockets. Israeli forces seized sparsely populated areas in northern Gaza. Israeli troops took over three six-floor buildings on the outskirts of Gaza City, taking up rooftop positions after locking residents in rooms and taking away their cell phones, a neighbour said, quoting a relative in one of the buildings before his phone was taken away. Black smoke from tank shells and windswept dust billowed in the air over Gaza City, while white smoke from mortar shells rose in plumes above a main road leading to northern Gaza that the Israeli military seized on Sunday, cutting off Gaza's north from its south. Explosions could be heard in Gaza City as aircraft attacked buildings. The streets of Gaza City, home to 400,000 people, were almost empty. Unmanned Israeli planes and Apache helicopters circled overhead. Israel has three main demands: an end to Palestinian attacks, international supervision of any truce and a halt to Hamas rearming. Hamas remained defiant. "Victory is coming, God willing," the movement's senior leader in Gaza, Mahmud Zahar, said in a television address. Hamas remained defiant. "Victory is coming," the movement's senior leader in Gaza, Mahmud Zahar, said in a television address in which he praised "the most beautiful performances" of the group's armed wing. "Crush your enemy," he urged. Meanwhile in Riyadh, Saudi Arabia's cabinet headed by King Abdullah on Monday blasted the international community for condoning the Israeli attacks on the Gaza Strip, a statement on the SPA news agency said. "The international community remains silent, and is failing in an unprecedented manner to deal with the Israeli violations," said the statement issued following the cabinet's weekly meeting. "The brutal war Israel is waging on the Gaza Strip, the mass punishment and the attacks on unarmed civilians go against all principles of humanity," the statement added. Arab states plan to introduce a new draft resolution in the UN Security Council aimed at securing an immediate end to the "Israeli aggression" in the Gaza Strip, Palestinian foreign minister Riyad al-Malki said on Monday. Meanwhile, Iranian industry ministry on Monday ordered the suspension of all trading by foreign firms "whose shares could be owned" by Israelis in response to the Israeli assault on Gaza, the ISNA news agency reported on Monday.