Israeli forces are reportedly moving slowly into Gaza's most densely populated areas, as air and ground attacks continue against Hamas.
The BBC reports some reservists are in action on the ground, but the army denies escalating the war to a "third phase" - an all-out push on Gaza City and other towns.
Fewer air strikes were carried out on Sunday night - 12 compared with as many as 60 on previous nights. At least nine rockets or mortars were fired on Israel from Gaza.
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 elements were in place for a ceasefire agreement.
There were reports of fierce fighting around Gaza City ahead of a daily three-hour truce to allow aid deliveries to Gaza.
Israeli military spokeswoman Maj Avital Leibovich said troops were continuing their advance into urban areas.
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.
On Sunday, Israel reportedly dropped new leaflets into Gaza and left phone messages warning Gazans to stay away from areas used by Hamas.
No ceasefire yet
Both Hamas and Israel have rejected a UN resolution last week calling for immediate ceasefire.
Israeli Prime Minister Ehud Olmert said "nobody should be allowed to decide for us if we are allowed to strike".
Aid agencies say the 1.5 million residents of Gaza are in urgent need of food and medical aid.
Air raids began on 27 December, after Hamas ended a ceasefire on 19 December. Israeli ground forces entered Gaza on 3 January.
Palestinian medical sources say the total number of dead is more than 900.