The death toll in Israel's assault on the Gaza Strip passed 360 as the territory was bombarded throughout the night by the heaviest barrage of tank shells since the beginning of the offensive twelve days ago.

Thirty-one bodies were brought to hospitals on Sunday morning, medics told Al Jazeera, and the number was expected to rise as ambulances were able to reach neigbhourhoods east of Gaza City.

Hundreds of people who had been trapped by overnight bombardment were entering Gaza City on foot in the morning as shelling could still be heard, Al Jazeera's Stefanie Dekker reported.

Israel announced on Saturday that four of its soldiers were killed in combat with Palestinian fighters, bringing the total death toll on the Israeli side to seven.

Al Jazeera's John Hendren, reporting from Jerusalem, said two soldiers were killed during an exchange of gunfire as they fought Palestinians in tunnels near the Israel-Gaza border.

A Palestinian fighter was also killed while several others escaped back into a tunnel into Gaza, our correspondent said.

Earlier on Saturday, an Israeli Bedouin was killed when a rocket hit his encampment in southern Israel in an attack which also wounded four of his family, among them two young children, police said.

Israel began its offensive with air strikes on July 8 in response to rocket fire from Gaza. It says Hamas military installations are being targeted, but an overwhelming majority of those killed and injured have been civilians.

While shelling focused on northern Gaza on Saturday, heavy Israeli artillery attacks also took place across other areas of the Hamas-ruled territory. Drones, jets and attack helicopters patrolled the skies.

Aid convoy blocked

In another development on Saturday, agencies said Egyptian soldiers in north Sinai prevented an aid convoy of activists from reaching the Rafah border crossing with the Gaza Strip.

An army officer at the Balloza checkpoint, one of many along the desert highway to Rafah, told an AFP correspondent that the security situation in the peninsula was too unstable to allow the convoy of 11 buses and 500 activists to pass.

There was a brief scuffle between some activists and soldiers but no arrests were made.

Egypt usually keeps the crossing closed, citing a counterinsurgency operation against fighters in north Sinai, but has allowed entry to Palestinians wounded in the 12-day conflict between Hamas and Israel.

The Egyptian military had earlier said it was sending 500 tonnes of food and medical aid to Gaza.

Hamas has refused to accept a ceasefire with Israel until it receives guarantees that border crossings to Gaza - all but one under Israeli control - will be opened.

Success 'not guaranteed'

The ground offensive is a new phase in Israel's Operation Protective Edge operation which the military said would destroy tunnels used by Hamas.

Benjamin Netanyahu, the Israeli prime minister, said the ground operation was necessary to deal with the tunnels, but admitted there was "no guarantee of 100 percent success".

The offensive failed to prevent an incursion by a tunnel into Israel by Qassam Brigades fighter on Friday. The attack was foiled by the Israeli military, however, with one fighter killed.

On the diplomatic front, the Palestinian and Israeli UN ambassadors traded blame for the violence, with Israel's Ron Prosor insisting no other country would "tolerate ... terrorist" rocket fire at its citizens.

Meanwhile, Qatar will host a meeting between Palestinian President Mahmoud Abbas and UN Secretary-General Ban Ki-moon on Sunday to try to reach a ceasefire agreement with Israel.

Due to take place in Doha, the meeting will be headed by the Gulf state's emir, Sheikh Tamim bin Hamad Al Thani, who has been acting as a "channel of communication" between Hamas and the international community, a senior source familiar with the matter told Reuters news agency.

"Qatar has presented Hamas' requests to the international community, the list has been presented to France and to the UN, the talks tomorrow will be to further negotiate these conditions."

A UN statement said Ban will be travelling to Doha, Kuwait City, Cairo, Jerusalem, Ramallah and Amman and that other stops might be added.

Ban would help Israelis and Palestinians "in coordination with regional and international actors, end the violence and find a way forward," Jeffrey Feltman, UN under secretary-general for political affairs, told the Security Council.