Israel said its forces were pushing deep into Gaza City, where residents said tanks were positioned on the outskirts for a potential storming of Gaza's urban heartland.

"For the first time in decades, IDF is fighting in the heart of Gaza City. At the heart of terrorism," Major General Yaron Finkelman, commanding officer of the Southern Command of the Israeli Defence Forces, told reporters near the Gaza border.

"Every day and every hour the forces are killing militants, exposing tunnels and destroying weapons and continuing onward to enemy centres."

Israel previously said it had surrounded Gaza City, home to around a third of the Gaza Strip's 2.3 million people, and would soon attack it to annihilate Hamas fighters who assaulted Israeli towns across the border one month ago.

There was no indication on the ground that Israeli forces had thrust en masse further into the city, but a spokesperson for the military, Richard Hecht, suggested that the encircling troops could be making raids inside.

Asked whether such raids had taken place, he said: "I'm not going to talk about how we are operationally acting from within our encirclement around Gaza City. You are in the right direction, that's all I can say."

The military wing of Hamas said its fighters were inflicting heavy losses and damage on advancing Israeli forces.

It was not possible to verify the battlefield claims of either side.