Among the latest victims were a mother and her four young children, killed in an Israeli air strike on their home in Gaza.
Four Israeli civilians have been killed and two injured by Palestinian rocket attacks.
The International Red Cross has urged Israel and Hamas to stop targeting civilians.
The military wings of rival Palestinian factions in Gaza have united to fight against the advancing Israeli troops. One Israeli soldier has been killed and 49 wounded.
On the diplomatic front, a Hamas official said a delegation would head to Cairo on Monday, "answering an Egyptian invitation to hold discussions" on a ceasefire.
The talks are set to coincide with the arrival of Nicolas Sarkozy, the French president, in the region, to push for a European-backed ceasefire.
The UN Security Council is also set to meet on Monday to discuss the crisis following an emergency session on Sunday that failed to produce a resolution or even a statement calling for a halt to the fighting.
Israel's ground offensive launched on Saturday followed eight days of intense bombardment of the Gaza Strip, purportedly aimed at ending cross-border rockets being fired by Hamas fighters from the territory into southern Israel.
An undaunted Hamas 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.
Shimon Peres, the Israeli president, rejected the possibility of a ceasefire but said Israel did 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 on Sunday.
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.
Christopher Gunness, the UN Relief and Works Agency (Unrwa) spokesman, said the idea that there was no humanitarian crisis in Gaza, was absurd.
"The organisation for which I work - Unrwa - has approximately 9,000 to 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.
Al Jazeera's Ayman Mohyeldin, reporting from Gaza City, said power lines have been cut throughout Gaza and more than 250,000 people in the northern part of the territory were without electricity.
Witnesses in eastern Gaza told Al Jazeera that soldiers had begun house to house operations, moving from building to building. They had also taken positions on top of many of the rooftops in that area, the witnesses said.
|Barak said the operation would be "expanded and intensified as much as necessary" [AFP]
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 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."