Israeli tanks shelled Gaza City today and ground troops thrust deep into a crowded neighbourhood for the first time.
Aircraft struck 70 targets in Gaza overnight - but the Israeli military said 14 rockets were fired from the territory this morning.
The latest attacks sent terrified Gaza residents fleeing for cover, ratcheting up the pressure on Hamas to accept a proposed ceasefire to end the devastating Israeli offensive.
It was not clear if the intensified assault on Gaza City signalled a new phase in the three-week-old Israeli campaign, which has already killed more than 1,000 Palestinians.
The advance into Gaza City's Tel Hawwa neighbourhood and the shelling of the city centre came as UN chief Ban Ki-moon was due to arrive for meetings with Israeli and Palestinian leaders.
He was coming from Egypt, which has been working with Israel and Hamas to secure at least a temporary halt in fighting.
Israel launched the offensive on December 27 in an effort to stop militant rocket fire from Gaza that has terrorised hundreds of thousands of Israelis.
It says it will press ahead until it receives guarantees of a complete halt to rocket fire and an end to weapons smuggling into Gaza from neighbouring Egypt.
Rocket fire has fallen off dramatically since, but not ceased. Thirteen Israelis have been killed since the offensive began.
Thousands of Tel Hawwa residents fled their homes today, many clad only in their pyjamas, and some wheeling elderly parents in wheelchairs, one of them with an oxygen tank.
Others stopped journalists' armoured cars and ambulances pleading for someone to take them to a UN compound or to relatives' homes.
Rasha Hassam, a 25-year-old engineer, ran out of her apartment building carrying her screaming six-year-old daughter, Dunia.
"God help us, God help us, where can we flee?" she cried. "All I want is to get my poor child away from here. We want to survive."
Thousands of others were trapped in Tel Hawwa's high-rise buildings by the fire, too afraid to attempt to flee.
Israeli aircraft struck some 70 targets overnight, including weapons positions, rocket squads and a mosque in southern Gaza that allegedly served as an arsenal, the military said.
One target was the Islamic University in Gaza City, a Hamas stronghold,
Clouds of white smoke covered the eastern section of the city while a pillar of black smoke towered over the western portion following air, tank and naval fire that set houses and farmlands ablaze.
Human rights groups have accused Israel of unlawfully using white phosphorous shells against populated areas. The weapon can burn anything it touches and is used to illuminate targets at night or create a smoke screen for day attacks.
The Israeli military has said only that it uses munitions in accordance with international law, and the International Committee for the Red Cross has said it has no evidence that Israel has improperly used the shells.
Mr Ban launched a week-long trip to the region on Wednesday, hoping to help secure a truce a week after the UN Security Council passed a cease-fire resolution.
He will also meet with Palestinian leaders in the West Bank, where President Mahmoud Abbas governs. He will not visit Gaza, which has been ruled by Hamas since it expelled forces loyal to Abbas in June 2007. The international community does not recognise Hamas' government.
Israel's chief negotiator, Amos Gilad, planned to fly to Egypt on today, a senior defence official said, while Israel also sent a senior diplomat to Washington to discuss international guarantees that Hamas will not rearm - a key Israeli demand.
World pressure on Israel to halt its offensive has increased.
The conflict has killed more than 1,000 Palestinians, about half of them civilians, including 300 children and teenagers, while 4,500 Palestinians have been wounded according to medical officials.
Syrian President Bashar Assad told the BBC Hamas was ready for a "sustainable cease-fire," and was the first indication that Syria, which hosts the exiled Hamas leadership, was involved in the cease-fire effort.
Egypt has been pressing both sides to accept a 10-day truce while a more comprehensive accord can be worked out.
But Egypt's UN Ambassador Maged Abdelaziz told a UN Security Council meeting yesterday that neither side had accepted the Egyptian plan. "Each believes that it will emerge victorious", he said.
Israel has made clear that the Cairo talks are key to determining whether it widens its offensive.
Under the Egyptian proposal, Hamas would back off its demand that Israeli troops withdraw from Gaza and borders be opened immediately as part of any halt in fighting.
Instead, Israeli forces would remain in place during a 10-day truce until details on border security are worked out.
A senior Israeli official said it was far from certain Israel would accept the deal. He said Israel welcomed many parts of the plan, but was afraid Hamas would not respect a cease-fire as long as troops are in Gaza.
Israel rejects charges that its blockade has caused a humanitarian crisis, saying it has let more than 1,000 truckloads of supplies into Gaza during the fighting. Almost 200 trucks were due to enter Gaza today, including food, medical supplies, fuel and animal feed.