Diplomatic pressure for a ceasefire in Gaza intensified on Sunday as Israel expanded its ground offensive and the death toll in the 11-day conflict climbed to more than 350.

The Israeli military said in a statement on Sunday that it had sent additional forces into the Palestinian enclave where at least 50,000 people had to flee their homes in the face of the military assault from ground, air and sea.

Gaza officials said at least 345 Palestinians, many of them civilians, have been killed in the 13-day conflict. On Israel's side, five soldiers and two civilians have died.

Two Israeli soldiers were killed in a cross-border attack by Hamas militants on Saturday, the army said. Military officials said four other soldiers were wounded in the raid by fighters who had used a concealed tunnel to reach Israel. One Hamas gunman was killed, while the rest of the group managed to escape back into Gaza.

Israel's bombardment of Gaza intensified on Saturday night as a handful of areas were hit every few seconds with tank and rocket fire. With Israel suggesting that its ground offensive could last two weeks, the UN secretary general, Ban Ki-moon, travelled to the region to add his weight to efforts to broker a truce between Israel and Hamas.

The Egyptian government restated a proposal it had made on Monday, which was accepted by Israel but dismissed by Hamas. Israel launched the ground invasion following Hamas's rejection. "This initiative still presents the chance for the two sides to cease fire, ending the bloodshed," said Egypt's foreign minister, Sameh Shukri. "It meets the needs of both sides. We will continue to propose it. We hope both sides accept it." Laurent Fabius, the French foreign minister, said a ceasefire was "an urgent imperative", adding that his government fully backed the Egyptian initiative, which is also supported by the Arab League. "The absolute priority is a ceasefire, but it must guarantee a lasting truce," Fabius said in Cairo, after meeting the Egyptian president, Abdul Fatah al-Sisi.

Hamas has refused to agree to a ceasefire without preconditions on the release of prisoners arrested in the West Bank and the opening of crossings from Gaza to Egypt and Israel. Senior Hamas official Ghazi Hamad told Channel 4 News on Saturday that Hamas would continue to fire rockets until Israel agreed to its demands.

Qatar and Turkey, seen as allies of Hamas, were also attempting to broker a ceasefire, with the Qatari foreign minister, Khalid bin Mohammed al-Attiyah, reportedly tabling a proposal reflecting Hamas's stance.

In Gaza, Israeli tanks and bulldozers were clearing a wide strip of land inside the perimeter fence as troops continued to hunt for openings to cross-border tunnels dug by militants. The Israeli Defence Forces (IDF) said it had found more than a dozen tunnels since the ground offensive started. The UN said the number of internal refugees had more than doubled since the start of the invasion, to at least 50,000, with the number expected to rapidly rise. The World Food Programme was stepping up efforts to distribute supplies to Palestinian civilians caught in the fighting.

Thousands of pro-Palestinian demonstrators marched to the Israeli embassy in London , calling for an end to military action in Gaza.