Israel forces are moving into Gaza's most densely populated areas, even as United Nations Secretary-General Ban Ki-moon demanded that Israel and Hamas stop fighting immediately.
The Israeli army denies it is escalating the war to an all-out push on Gaza city and other towns. But Israel's bombardment by land, sea and air has continued throughout the night, with shelling and airstrikes hitting Gaza City, Rafah and elsewhere.
Both Israel and Hamas, which controls the Gaza Strip, have ignored a call by the UN Security Council last week for an immediate ceasefire. However, Mr Ban insists that the resolution must be observed and says "too many people have died".
He is due in Cairo on Wednesday for talks with Egyptian President Hosni Mubarak, Foreign Minister Ahmed Abul Gheit and Arab League chief Amr Mussa.
However, Mr Ban indicated he would not visit Gaza or have direct contact with leaders of Hamas.
Egypt is trying to broker a ceasefire between Hamas and Israel, but Lebanese sources say Hamas is set to reject Egypt's proposals to end Israel's 18-day-old offensive,
The sources say Hamas negotiators who returned to Cairo on Monday night after consulting their leaders in Damascus would relay Hamas' response in talks on Tuesday with Egypt's intelligence chief, Omar Suleiman.
Hamas is reportedly opposed to three key elements in the proposal, worked on by Egypt and international diplomats in recent days.
"Hamas opposes a long-term truce - the Egyptians speak of 15 years - and it is opposed to any ceasefire being set without it being accompanied by immediate pullout of Israeli troops from newly occupied positions in Gaza, and the presence of foreign observers on the Rafah crossing point," one source said.
Israel launched its offensive on 27 December with the declared aim of stopping Hamas firing rockets into southern Israeli towns and cities.
Palestinian officials says more than 900 people have been killed - including 300 children - and 4,000 wounded. Israel says 10 soldiers and three civilians have died in the conflict.
US abstains in UN vote
On Tuesday, the United States abstained from voting on a Gaza ceasefire resolution at the United Nations.
Fourteen of the 15 UN Security Council members voted in favour of a British draft resolution calling for an immediate ceasefire in Gaza, followed by a full Israeli withdrawal.
US Secretary of State Condoleezza Rice said it supported the contents of the resolution despite abstaining in the vote.