"This is the 18th day of the Israeli aggression against our people, which is becoming more ferocious each day as the number of victims rises," Palestinian president Mahmud Abbas said as terrified Gaza residents fled for their lives.
"Israel is keeping up this aggression to wipe out our people over there," added Abbas, speaking from his base in the West Bank.
Israeli special forces backed by tanks and air strikes barrelled their way ever deeper into Gaza's City, advancing several hundred metres into several neighbourhoods in the south, witnesses and correspondents said.
The thud of tanks shells and the rattle of gunfire echoed through much of the day while bombing raids in the border town of Rafah sent hundreds of people fleeing onto the streets.
"There are continuous airstrikes along the Egyptian border -- about 60 families have all fled their houses which are situated several hundred metres from the border," Jawad Harb, a Palestinian working for the international aid agency CARE, said as a series of deafening blasts echoed in the background.
Palestinian medical sources said that 54 more people had been killed in the latest day of fighting, bringing the overall toll to around 960 Palestinians.
On the Israeli side, 10 soldiers and three civilians have been killed in combat or by rocket attacks since December 27, when the Jewish state began its deadliest ever offensive on Gaza, ruled by Hamas since mid-2007.
Israel's military chief acknowledged that Israeli troops faced "complicated" conditions in Gaza City, home to more than half a million Palestinians, where Israel has little combat experience.
A Hamas delegation is currently in Cairo for talks on a Western-backed proposal drawn up by President Hosni Mubarak on how to end the fighting.
A senior official in Cairo indicated Egypt was getting increasingly frustrated at Hamas's response so far to its initiative.
"We're working seriously with Hamas, we need to end the vagueness and they need to say 'yes', now, to our plan," the Egyptian diplomat said on condition of anonymity.
Senior Hamas leader Mussa Abu Marzuk acknowledged the movement had "substantial observations" on the initiative but said there was "still a chance" that Hamas would accept the plan.
"If the initiative is accepted, it will be in accordance with the position set out by Hamas at the start, namely an Israeli withdrawal, a ceasefire and the opening of the crossing points" between Gaza and Israel, Abu Marzuk said.
Hillary Clinton, due to take over as US Secretary of State in a week's time, said President-elect Barack Obama's administration would make "every effort" to forge Israeli-Palestinian peace.
However she ruled out holding talks with Hamas.
Meanwhile, the US military had to cancel a planned shipment of munitions from a Greek port to a US warehouse in Israel due to objections from Athens.
The Greek government “had some objection to offloading that shipment in their country," spokesman Geoff Morrell told a news conference.
Egypt and Saudi Arabia blocked a proposal by Qatar for an extraordinary summit on the crisis later this week by saying discussions should instead take place at a summit in Kuwait already scheduled for January 19.
UN chief Ban Ki-moon, who was headed to the Middle East on Tuesday, also called on Israel and Hamas to immediately stop the fighting, saying "too many people have died."
Aid agencies have warned of a growing humanitarian crisis in the territory where the vast majority of the 1.5 million population depends on foreign aid and that is already reeling from months of a punishing Israeli blockade.
The charity Save the Children estimated only an eighth of the life-saving supplies of food and medicines needed by Gaza's population have crossed into the territory since December 27.
"More than a million people in Gaza rely on aid coming in by truck, but so far the amount coming in is nowhere near what is needed," said the charity's spokesman Benedict Dempsey.
"The amount of aid that has crossed into Gaza so far is pitiful."