Doctors at Gaza's central Shifa hospital told local radio that around six Palestinians had been killed and some 30 injured overnight. The death toll in Gaza since December 27, when Israel first launched airstrikes on the enclave, is reported to have risen to over 920, with over 4,000 injured.
Israel's Army press service said that eight soldiers had been wounded, one seriously, in the fighting, which has claimed the lives of 10 Israeli troops and three civilians.
In a rare televised broadcast, Ismail Haniya, one of the leaders of the Hamas movement, which seized control of Gaza in June 2007, said that the fighting would continue, but added that the Islamists were prepared to examine any initiative "to stop the aggression and lift the blockade" on Gaza.
Israeli Prime Minister Ehud Olmert said, however, Israel would only call a halt to its operations in Gaza if Palestinian militants stopped firing rockets on Israel's southern territories and ceased smuggling arms into the enclave.
The premier said "If these two conditions are met, we will end our operation in Gaza."
Meanwhile, the search for a diplomatic solution is continuing in Cairo where Egyptian authorities are holding parallel talks with the Israelis and Palestinians.
And UN Secretary-General Ban Ki-moon is due to arrive in the Middle East on Wednesday to meet leaders from the region to seek an end to the violence, which is threatening the densely populated Gaza Strip, home to some 1.5 million Palestinians, with a human catastrophe.
"To both sides, I say. Just stop, now," the UN chief said, "Too many people have died. There has been too much civilian suffering."
On Thursday the UN Security Council adopted a resolution, with just the U.S. abstaining, calling for "an immediate, durable and fully respected ceasefire, leading to the full withdrawal of Israeli forces form Gaza."