One Israeli military officer told The Associated Press that Hamas fighters often operate in small groups of up to four and have largely refrained from confronting Israeli troops at close range.

"Their strategy has mainly been to use lots of booby-traps, shooting guns and missiles from afar," the Israeli officer said on condition of anonymity because he was not authorized to speak to the media.

"Soldiers are taking lots of precautions, they are being more careful than the army has ever been before in any war," he said. "Soldiers shoot at anything suspicious, use lots of firepower, and blast holes through walls to move around."

Gabi Ashkenazi, chief of staff of the Israeli military, said Hamas militants also have put on Israeli military uniforms to try to approach troops and carry out suicide bombings.

Ahead of the U.N. chief's arrival, Israeli U.N. Ambassador Gabriela Shalev wrote him a letter charging that Hamas is "deliberately endangering civilians" in Gaza. She claimed that Hamas operates a command center under Shifa Hospital, Gaza's largest, and militants "routinely fire from inside the houses of civilians who are held as hostages, prevented by Hamas from leaving."

Hamas, which is backed by Iran, cannot hope to score a battlefield victory over the powerful Israeli military, but mere survival could earn it political capital in the Arab world as a symbol of resistance to the Jewish state. Lebanon's Hezbollah, another Iran-backed group, largely achieved that goal in its 2006 war with Israel.

On Tuesday, a Gaza resident said he saw Hamas militants in civilian clothing firing rockets from the southeastern corner of the territory. He spoke by telephone and requested anonymity because of the sensitivity of the information.

Israel says it will push forward with the offensive until Hamas ends all rocket fire on southern Israel, and there are guarantees the 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.

"We will not allow our enemy to gain any political achievement from this war on Gaza," said Salah Bardawil, a Hamas envoy in Egypt.

Much of the ongoing 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 bombed suspected tunnel sites throughout its campaign.

One resident, Khader Mussa, said he fled his house while waving a white flag as Israeli forces advanced. He spent the night huddling in the basement of a relative with 25 other people, including his pregnant wife and his parents.