Al Jazeera's Sherine Tadros, reporting from Gaza City, said there was an intensification of Israeli ground operations, with reservists moving in to support regular ground forces.
The AFP news agency reported Israeli tanks, supported by warplanes, had moved into several southern neighbourhoods of Gaza City and that Palestinian fighters were responding with mortar fire.
A spokesman for the Palestinian health ministry said dozens of calls for ambulances had been received, but none could be dispatched because of the fighting.
Combat continued despite another day of pleas from both the United Nations and the European Union to stop the violence, which has so far killed 940 Palestinians and wounded 4,300 others.
Civilians make up around 40 per cent of casualties, with the majority of those being women and children.
Expressing frustration at the failure of both sides to adhere to a legally binding UN resolution calling for an immediate ceasefire, Ban Ki-moon, the UN secretary-general, said he planned to step up diplomatic efforts to end Israel's air and ground offensive in Gaza and Hamas rocket fire into southern Israel.
"To both sides, I say: just stop, now," the UN chief told a news conference on Monday. "Too many people have died. There has been too much civilian suffering. Too many people, Israelis and Palestinians, live in daily fear of their lives."
But Ehud Olmert, the Israeli prime minister, said the offensive which includes the latest deployment of reservists into Palestinian neighbourhoods, must continue until Hamas is completely disarmed.
"To both sides, I say: just stop, now"
He said the military operation would end once Hamas's military wing halted its rocket attacks.
"We want to end the operation when the two conditions we have demanded are met: ending the rocket fire and stopping Hamas's rearmament. If these two conditions are met, we will end our operation in Gaza," he said in the southern Israeli town of Ashkelon.
Al Jazeera's Ayman Mohyeldin reporting on the devastation in Rafah late on Monday said the continuous shelling had reduced the city to rubble and the Israeli military had been dropping leaflets warning local residents to flee.
He said the human suffering was compounded by the 18-month Israeli blockade that had led to a food and fuel shortage.
Al Jazeera's Zeina Awad, reporting from the Israel-Gaza border, said there were no signs of the war ending despite the huge humanitarian toll on the residents.
|Israeli reservists were deployed to support regular forces in Gaza [EPA]
The Israeli military said air raids were carried out on at least 25 targets across the Gaza Strip and Shimon Peres, the Israeli president, said on Monday that the army had "achieved in 16 days what no other country in the world fighting terror has done in 16 years".
But the Palestinian fighters fired nearly 30 rockets across the border into southern Israel on Monday, according the an Israeli army spokesman, and Hamas said it would continue to battle Israeli troops inside Gaza.
Ismail Haniya, the Hamas leader and ousted Palestinian prime minister, said from Gaza City that Israel would not emerge victorious.
"This holy blood that has been spilt will never be in vain, it will make the victory. The children's and women's blood and bodies will be a curse which will haunt this occupation," he said.
Khaled Meshaal, Hamas's political leader in exile, said: "The Palestinian resistance is standing steadfast on the battlefield as it is in the political arena.
"The resistance cannot be broken in the face of the Israeli aggression, nor can our resolve despite the deep wounds, the great pains, the massacres, the destruction, the punishments and mass killings."