Smoke rises during Israeli bombardment of the Gaza Strip on Sunday amid ongoing battles between Israel and the Palestinian Hamas movement. AFP

Hamas said it was engaged in "heavy fighting" with Israeli troops inside northern Gaza on Sunday, as besieged residents were again warned to flee southward.

After weeks of ferocious airstrikes, Israel has declared a new "stage" in a war that Prime Minister Benjamin Netanyahu warned would be "long and difficult".

Late on Sunday Israel's military released footage that purported to show a significant number of tanks, infantry and artillery operating in Palestinian territory.

The military claimed to have struck more than "450 targets, including operational command centres, observation posts, and anti-tank missile launch posts".

Hamas said its Ezzedine Al Qassam Brigades were already "engaged in heavy fighting... with the invading occupation forces".

With a fierce door-to-door urban war expected, Israeli army spokesman Daniel Hagari told Palestinian civilians to go south "to a safer area".

It is now 23 days since Hamas gunmen launched a wave of bloody cross-border raids against homes, communities, farms and security posts inside Israel.

An estimated 1,400 people, mostly civilians, were killed and 239 people were taken hostage, according to the latest Israeli tallies.

This photo shows the Israeli army tanks and buldozers crossing the border into Gaza on Sunday. AFP

Israel has vowed to free the hostages, track down those responsible and "eradicate" Hamas, a Palestinian Islamist movement that has governed Gaza since 2007.

But there is deep and growing international concern about the toll of Israel's campaign on Gaza's two-plus million residents.

The territory is under siege, with people unable to leave and only a limited amount of humanitarian aid allowed in.

Meanwhile, Israel has carried out one of the most intense bombing campaigns in recent memory.

The Hamas-run health ministry in Gaza says more than 8,000 people, mainly civilians and half of them children have already been killed.

Agence France-Presse

Food, water, medicine

Inside Gaza's maze of streets, rubble and hulled-out buildings, there is a growing sense of panic, fear and desperation.

Ibrahim Shandoughli, a 53-year-old from Jabaliya in northern Gaza, asked why he would head south when that area is also being bombed.

Israeli troops gather near the border with Gaza before entering the Palestinian strip on Sunday. AFP

"Where do you want us to evacuate to? All the areas are dangerous," he said.

Etidal al-Masri was among those who fled after Israel told residents in the north to leave.

But she still struggles to find even the basics amid shortages of food, water and medicine.

Gazans "must now queue for bread, toilets and even for sleep", she said.

Agence France-Presse