The Israeli assault, codenamed "Operation Cast Lead", has killed more than 507 Palestinians and wounded more than 2,400 others. Four Israelis have been killed by the Hamas rocket strikes in the same time.
Among the latest victims were a mother and her four young children, killed in an Israeli air strike on their home in Gaza.
Also killed in Israeli shelling was a Palestinian paramedic, the Oxfam aid agency said. Another paramedic lost his leg when a shell struck an ambulance.
An undaunted Hamas, however, has vowed to fight back and defeat the Israeli forces. A spokesman for Ezzedine al-Qassam Brigades, the armed wing of the Hamas, told Al Jazeera on Sunday that Israeli troops faced death or capture.
"The battle has just started and the enemy should endure the consequences and results. They should be ready for the bad news coming from the Gaza Strip," Abu Obeida, a spokesman, said.
Hamas said it had captured two Israeli soldiers but the Israeli army denied that.
While the UN secretary-general called for an immediate end to the operations, the Security Council failed to agree on a resolution calling for a ceasefire after an emergency meeting.
Shimon Peres, the Israeli president, has meanwhile rejected the possibility of a ceasefire but said Israel does not intend to occupy Gaza.
"We don't intend neither to occupy Gaza nor to crush Hamas, but to crush terror. And Hamas needs a real and serious lesson. They are now getting it," Peres said in an interview.
Al Jazeera's Sherine Tadros, reporting from the Shifa hospital in Gaza City, said doctors were struggling to cope amid low supplies and the rising number of wounded.
She said the scene was chaotic, with doctors treating the injured on the floor.
Fears of a humanitarian crisis have also grown in recent days, as the strip, home to 1.5 million people, is already suffering shortages of fuel, food and medical supplies due to a two-year economic blockade imposed by Israel.
The International Committee for the Red Cross said on Sunday its medical emergency team had been prevented for a third day from entering the territory.
Egypt has also completely closed the Rafah crossing, cutting off aid supplies to the territory.
The UN has warned that there were "critical gaps" in aid reaching Gaza, despite claims from Tzipi Livni, the Israeli foreign minister, that there was no crisis and that aid was getting through.
However, Christopher Gunness, the UN Relief and Works Agency (Unrwa) spokesman said the idea that there is no humanitarian crisis is absurd.
"The organization for which I work - Unrwa - has approximately 9-10,000 workers on the ground. They are speaking with the ordinary civilians in Gaza... People are suffering. A quarter of all those being killed now are civilians. So when I hear people say we're doing our best to avoid civilian casualties that rings very hollow indeed."
Elsewhere in the strip, heavy artillery, tracer fire and rockets could be heard while reports said Israeli troops had reached the northern towns of Beit Lahiya and Beit Hanoun.
Soldiers and fighters were also locked in gun battles east of the Hamas stronghold of Zeitoun.
'Fear and terror'
Ayman Mohyeldin, Al Jazeera's correspondent reporting from Gaza City, said: "Perhaps the most significant military development on the ground is that Gaza has now actually been split into two.
"A column of Israeli tanks and artillery, and armoured personnel vehicles has made its way through from the eastern part of Gaza, reaching as far as the Mediterrannean sea on the Western part, essentially splitting Gaza.
"That area, mostly in the former settlement of Nitzerim, it was an open area after Israel withdrew the settlement, so they were able to make strong advances all the way across Gaza, essentially cutting off the northern part from the southern part."
Mohyeldin said that the scene in Gaza was one of "fear and terror".
He said power lines have been cut throughout Gaza and more than 250,000 people in the northern part of the territory were without electricity.
"The biggest concern is a ground invasion could result in urban warfare," he said.
|The Israeli defence minister said Israel
had weighed all options before the raids [AFP]
Witnesses in eastern Gaza told Al Jazeera that soldiers have begun house to house operations, moving from building to building. They have also taken positions on top of many of the rooftops in that area.
Al Jazeera's Jacky Rowland, reporting from the Israeli side of the border, said the authorities there have been extremely tight-lipped about the operation.
However, the military has confirmed that at least 30 soldiers have been wounded, two of them seriously, in the fighting so far.
Israel extended its naval blockade of Gaza early on Sunday, from six nautical miles to 20 nautical miles, preventing humanitarian aid and protest vessels from trying to break the siege.
It also captured the Hamas-affiliated Al Aqsa TV and has been broadcasting messages telling Hamas leaders to give themselves up.
Around 9,000 military reservists have been called up to assist in the ground assault.
Ehud Barak, Israel's defence minister, said that the operation was aimed at forcing Hamas "to stop its hostile activities against Israel and bring about significant change".
"The operation will be expanded and intensified as much as necessary," Barak said on Sunday. "War is not a picnic."
Mark Regev, an Israeli government spokesman, told Al Jazeera that the "single aim" of the offensive was to halt Hamas rocket attacks into Israeli territory.
"Ultimately Hamas is solely responsible for this crisis and today they are paying a price for that," he said.