GAZA CITY: Palestinian families streamed out of Gaza City today, some crammed into pick-up trucks, others on foot, as Israeli forces pressed their assault on the territory's main urban centre.

Parents carried their children while the elderly hobbled along, an AFP journalist reported.

A man in a wheelchair and another on crutches were among the long line of people heading south under Israeli military orders.

The military has issued multiple evacuation warnings for Gaza City, but many residents have told AFP they have nowhere else to go, noting that Israel has repeatedly struck the area in the south where it has urged people to move.

The scenes of mass flight from Gaza City came as US Secretary of State Marco Rubio arrived in Israel in a show of support, despite an Israeli strike in Qatar this week.

The Israeli military's Arabic-language spokesman, Avichay Adraee, issued today a warning to those in Gaza's port area and Al-Rimal neighbourhood to evacuate immediately to a"humanitarian zone" in the south, where Gazans say there is no more space to pitch tents.

He had on Saturday said more than 250,000 Gaza City residents had already fled, while Gaza's civil defence agency said the figure was closer to 68,000.

Media restrictions in Gaza and difficulties in accessing many areas mean AFP is unable to independently verify the details provided by the civil defence agency or the Israeli military.

Prior to the latest assault, the United Nations had estimated that around a million people lived in and around the city, where it officially declared famine last month.

AFP footage showed exhausted families moving along the coastal road near Nuseirat south of Gaza City, with their belongings stacked high in vehicles.

In the city itself,"the bombardment hasn't stopped since dawn," said Umm Alaa Shaaban, 45, a resident of Tal al-Hawa district in Gaza City's southwest.

"We haven't slept all night... The sounds of shelling and explosions have not stopped until now," she told AFP.

According to Shaaban, the Israeli air force"bombed many houses... we were terribly afraid – my children screamed in terror.

"We don't know where to go. The bombardment is everywhere."

Mohammed Ghazal, 32, who fled from Gaza City's Shujaiya neighbourhood, also said the strikes were relentless.

"We are living in a state of panic and extreme fear. The shelling hasn't stopped since dawn, the explosions are intense and the shooting continuous," he told AFP.

"Israeli forces are using terrifying methods and escalating the bombardment to frighten us and force us to flee south."

In recent days, the Israeli military has targeted several high-rise buildings in Gaza City, saying they were being used by Hamas militants.

On Sunday, it said it had struck another high-rise where Hamas had set up"observation posts to monitor the location of... troops in the area."

AFP also saw an Israeli leaflet dropped on residents, telling them they were in a"dangerous combat zone" – a message the military has repeated for weeks.