Thousands are fleeing northern Gaza following a night of fierce bombardment as Israel expands a ground assault on day 13 of the deadliest violence in the enclave in five years.

With UN chief Ban Ki-moon arriving in the region on Sunday to add his weight to truce efforts, the Palestinian death toll hit 370 although medics said it was set to soar after a series of intense attacks to the north and east of Gaza City.

But the Islamist Hamas movement, the main power in Gaza, refused to yield in the face of the relentless air, sea and land attacks, continuing its own assaults which killed another two Israeli soldiers overnight, the army said.

• More innocent children killed than militants

As the warring sides showed no sign of giving up, diplomatic efforts to seek a truce were to intensify on Sunday with Hamas’s exiled leader Khaled Meshaal to meet Palestinian president Mahmud Abbas in Qatar to discuss an Egyptian truce proposal.

On the ground, the streets of the northern district of Shejaiya were filled with thousands of people fleeing for their lives after heavy shelling left casualties lying in the streets.

Smoke rises after an attack on Shejaiya. Photo: AAP

Ambulances were unable to reach much of the area along the border because of heavy fire, and emergency officials said there were reports of wounded trapped by the bombardment.

At Shifa hospital, casualties were being brought in by the minute, some in ambulances, but others in cars and trucks.

Among them were screaming children with shrapnel wounds. Fights broke out in the emergency room as hysterical parents banged on the walls in fear and sorrow.

At least 24 Palestinians were confirmed dead on Sunday even before the massive bombardment.

But as day broke, there were reports of multiple casualties in strikes on Shejaiya and neighbouring Zeitun, as well as in Jabaliya to the north, emergency services spokesman Ashraf al-Qudra said.

Seven Israelis have been killed so far, five of them soldiers. Four soldiers were killed on Saturday, among them two who died in militant raid inside Israeli territory.

Another was killed by an anti-tank missile while the fourth died in a firefight with a militant who had emerged from a tunnel and attacked troops, the army said.

Israel said its ground operation to destroy the network of tunnels used by militants to stage deadly cross-border attacks was to “expand” later on Sunday.

Israelis protest against the attacks on Gaza. Photo: Getty

“This evening, the ground phase of Operation Protective Edge expands, as additional forces join the effort to combat terror in the Gaza Strip and establish a reality in which Israeli residents can live in safety and security,” the army said.

Army spokesman Lieutenant Colonel Peter Lerner said since the ground operation began late on Thursday, 70 militants had been killed and 190 rockets had hit Israel.

Before dawn, an intensive artillery barrage struck areas east of Gaza City, killing at least two children, medics said, as the civilian death toll grew.

The increasing number of children killed in the conflict is causing a growing outcry, with a joint statement from NGOs War Child and Defence for Children International saying more children had been killed than militants.

Figures provided by the UN children’s agency on Sunday showed that at least 73 of the victims were under the age of 18.

– AAP