GAZA CITY, Gaza Strip — Israel's chief negotiator will go to Egypt for "decisive" talks on a cease-fire with Hamas, officials said Tuesday, as the sound of battles between Israeli troops and Palestinian militants rang out in the crowded streets of Gaza City.

With international outrage mounting over the toll on Gaza's civilians, Israel's decision to send Defense Ministry official Amos Gilad to Egypt on Thursday could be a signal of progress. Gilad had postponed the trip for days.

Diplomatic efforts to end 18 days of fighting have moved slowly, in part because of the wide gaps between Israel and Hamas, who do not negotiate directly.

Israel says it will push forward with the offensive until Hamas ends all rocket fire on southern Israel, and there are guarantees the Iranian-backed militant group will stop smuggling weapons into Gaza through the porous Egyptian border.

Hamas has said it will only observe a cease-fire if Israel withdraws from Gaza.

Much of the diplomacy focuses on an area of southern Gaza just across the Egyptian border that serves as a weapons smuggling route, making Egypt critical to both sides in any deal.

Israel wants smuggling tunnels along the border sealed and monitored as part of any deal, and has been bombing the tunnels throughout the campaign.

The push into the Tel Hawwa neighborhood was the farthest Israel has moved into Gaza City, and brought ground forces within a mile (1.5 kilometers) of the crowded city center. Palestinian hospital officials say more than 900 Palestinians, half of them civilians, have been killed over more than two weeks of fighting.

Palestinian rocket fire has been greatly reduced, but not halted altogether, since the offensive was launched. Some 15 rockets and mortar shells were fired toward Israel Tuesday, causing no injuries, the army said. A total of 13 Israelis have died since Dec. 27.

U.N. chief Ban Ki-moon was headed to the region Tuesday to press for a cease-fire, and a Hamas delegation resumed talks in Cairo with Egyptian intelligence officials.

Israeli military officials say that depending on what happens with what they described as "decisive" talks in Cairo, Israel will either move closer to a cease-fire or press on with an even tougher stage of its offensive. They spoke on condition of anonymity because they were discussing sensitive policy matters.

Prime Minister Ehud Olmert has vowed to press forward with an "iron fist," despite growing international calls for an end to the fighting.

Israel's army has largely avoided the difficult terrain of Gaza City's narrow alleyways and crowded neighborhoods.