Palestinians have been warned to leave areas close to Hamas facilities
The UN secretary general has implored Israel and Palestinian militants to halt the fighting in Gaza immediately.
Ahead of a trip to the region to push for a truce, Ban Ki-moon said too many people had died and there had been too much civilian suffering.
His call came as Israeli ground forces and tanks moved deeper into Gaza City, with a BBC producer there saying he could hear shooting from tanks.
Nearly 30 rockets or mortars were fired on Israel from Gaza on Monday.
Early on Tuesday, the 18th day of the conflict, Israeli troops advanced in the southern and eastern suburbs of Gaza City, backed by artillery and helicopters.
The western areas of the city came under shellfire from Israeli gunboats.
The Israeli military has denied a Hamas claim that it had destroyed two Israeli tanks.
An army spokesman told the BBC that "more than 60 targets were targeted by IAF [Israeli Air Force]" during the night.
Ban Ki-moon calls for an immediate ceasefire
But the Israeli military announced a three-hour ceasefire starting at 0900 local time (0700 GMT) to allow aid lorries into Gaza.
The truce also coincides with visits to the territory by UN and Red Cross officials.
Also on Tuesday, an Israeli army patrol in the West Bank came under fire from inside Jordan, the army said. No-one was hurt in the incident and the patrol returned fire.
Gaza 'not broken'
Prime Minister Ehud Olmert said Palestinian militants will keep on feeling Israel's "iron fist" as long as Hamas fires rockets at Israel.
But a senior Hamas leader, Ismail Haniya, said the group was "approaching victory".
"After 17 days of this foolish war, Gaza has not been broken and Gaza will not collapse," he said in a televised address from a secret location in Gaza.
Both Hamas and Israel rejected last week's UN Security Council resolution calling for an immediate ceasefire.
Palestinian medical sources say 910 people have been killed in Gaza so far, of whom 292 were children and 75 were women. Israeli officials say 13 Israelis, including three civilians, have been killed.
On Monday, casualty reports from Palestinian medics ranged from nine to 26 dead, while Israel said five of its soldiers had been injured, one of them seriously.
Israel is preventing international journalists from entering Gaza, making it impossible to independently confirm casualty figures.
"My message is simple, direct and to the point: the fighting must stop," Mr Ban told a news conference in New York ahead of his departure on Tuesday for the Middle East.
"In Gaza, the very foundation of society is being destroyed: people's homes, civic infrastructure, public health facilities and schools."
His diplomatic tour will see talks with the leaders of Egypt, Israel and Syria as well as the Palestinian president in Ramallah.
However UN officials say he will not be meeting representatives of Hamas, and it is not clear whether he will go to Gaza itself during his week-long trip.
Meanwhile reports suggest diplomatic efforts between Egypt and Hamas in Cairo are progressing.
After meeting Egyptian President Hosni Mubarak, Middle East Quartet envoy Tony Blair said the elements were in place for a ceasefire agreement.
"I am hopeful we can put an agreement together but it's going to have to be worked on very hard and it's got to be credible," he told journalists.
On Monday as Israel continued its air and ground offensive, Hamas said it had been involved in fighting with Israeli troops in several districts.
There were reports of fierce fighting around Gaza City ahead of the daily three-hour truce to allow aid deliveries to Gaza.
Some Israeli reservists are in action on the ground, but the army denied escalating the war to a "third phase" - an all-out push on Gaza City and other towns.
Reservists are reported to be securing areas gained in the fighting.
The chief military spokesman, Brig Gen Avi Benayahu, said thousands more - who would comprise a new, expanded phase in the ground operation if it was ordered - were still in training and had not been deployed.
Israel hopes the scale of its operation will greatly reduce the number of missiles fired from Gaza into southern Israel, while eroding support for Hamas.
As the fighting continued, a spokesman for the charity Save the Children said it was impossible for aid workers to do their jobs.
"We need the violence to stop. We need the attacks to stop. It's only when that happens that we will be able to operate," Benedict Dempsey said.
Aid agencies say Gaza's 1.5 million residents are in urgent need of food and medical aid.