The comments reflected a view among some Israeli officials that any lasting solution to the conflict would require either a breakthrough diplomatic accord that heavily restricts Hamas’s military abilities or a deeper ground assault into urban areas of Gaza, known here as a possible “Phase Three” of the war.
As the conflict entered its 19th day on Wednesday, three rockets fired from south Lebanon landed outside the town of Kiryat Shmona in northern Israel, but caused no casualties, the Israeli authorities said. The Israeli military said it fired back. It was not immediately clear who fired the rockets into Israel. A similar incident last week raised concerns briefly that a second front had opened in the war. But Hezbollah, the militant Shiite group which fought a war with Israel in 2006, quickly sought to assure the Lebanese government that it was not responsible.
In Gaza, the Israeli intelligence officials said, there were some signs that the military assault had undermined Hamas’s political cohesion, and that Hamas’s leaders in hiding inside Gaza were more eager for a cease-fire than group leaders in exile. They described this assessment as based on hard intelligence, presumably telephone intercepts.
A senior Egyptian official in Cairo said separately on Tuesday that representatives of Hamas had disagreed openly when participating in continuing Egyptian efforts to broker a cease-fire.
Inside Gaza, the military wing of Hamas has been hit “to a certain extent” with “a few hundred” Hamas fighters killed during the ground offensive that began midway through the war, the intelligence officials said. They spoke on condition of anonymity in return for discussing internal assessments of the conflict. Hamas is still able to launch 20 to 30 rockets a day, including 5 to 10 missiles of ranges longer than 20 kilometers, or about 12 miles, down by a third from the start of the war, the officials said.
Greater damage has been done to Hamas’s capacity to run Gaza, with a large number of government buildings destroyed over the course of the operation, they said.
The Israeli Army’s chief of staff, Lt. Gen. Gabi Ashkenazi, speaking to Parliament on Tuesday, said that “we have achieved a lot in hitting Hamas and its infrastructure, its rule and its armed wing, but there is still work ahead.”
“Hamas is in a very difficult position,” the Egyptian official said. “On the ground, their militants are not doing as good a job, not matching their rhetoric. But politically, they have been totally taken over by their sponsors.
“The guys inside are holding their ground, but they don’t want to continue the confrontation,” the official said. Egypt talks to Hamas but is not eager to see the radical Islamic group succeed in running a small statelet next door.
Israeli officials said they were delaying any expansion of the war until the negotiations succeeded or failed. But journalists and photographers along the Israeli border with Gaza said they saw large numbers of Israeli reservists moving into the territory, suggesting preparation for an intensified phase of the conflict.
On the eve of a visit to the region, which began in Cairo on Wednesday, the United Nations secretary general, Ban Ki-moon, demanded an immediate halt to the fighting in accordance with a Security Council resolution.
“Too many people have died,” Mr. Ban said, while Gazans are facing a humanitarian disaster. United Nations officials have said that three-hour daily humanitarian lulls are insufficient to provide enough food, medicine and other essentials to civilians. Israel said that 102 trucks carrying aid entered Gaza on Tuesday, with a total of 1,028 since the war began.
John Ging, director of operations in Gaza for the United Nations Refugee and Works Agency, who has been highly critical of the Israeli military action, said by video link that the fighting was extracting an unacceptably high toll on civilians.
“Tragically, the horror continues overnight,” he said. “Nineteen children killed and 52 injured last night. I would hope that would motivate those who can help.”
Hamas is capable of building rockets with an advanced propellant that can go up to 18 miles, the intelligence officials said, using chemicals and parts smuggled in from Egypt. Hamas also is using 122-millimeter rockets that are Chinese-made and supplied by Iran that can go almost 25 miles, they said.
But they assessed the probability that Hamas now has rockets capable of going farther than 25 miles as “very low.”
On Tuesday, Hamas fired 11 rockets and six mortar shells into Israel, the Israeli Army said.
General Ashkenazi said that Israeli aircraft had carried out more than 2,300 strikes since the offensive began on Dec. 27.
In Tuesday’s fighting, 18 Palestinian fighters and seven civilians were killed, part of the 971 Palestinians who have died, according to Gaza’s Hamas-run Health Ministry. Those figures are not thought to include many of the fighters killed since the ground war began.
Thirteen Israelis have died, including 10 soldiers. The Israeli military said one Israeli officer was critically wounded and two Israeli soldiers suffered light wounds in fighting overnight. They were hurt, the military said, after a bomb exploded in a booby-trapped house that they were searching.
General Ashkenazi said that Hamas fighters were using suicide bombers, sometimes women and sometimes dressed as Israeli soldiers, to try to get close to Israeli troops and kill them. One Israeli soldier was killed last week by a Hamas suicide bomber, the Israeli intelligence officials said. The method of the attack that caused the death had not been disclosed before.
Moussa Abu Marzouk, the exiled deputy to the Hamas political chief Khaled Meshal, told Al Jazeera television on Tuesday that while the organization had “serious reservations” about the Egyptian cease-fire plan, he believed that it might be accepted if changes were made.
“If the initiative is accepted, it will be in accordance with the position set out by Hamas at the start, namely an Israeli withdrawal, a cease-fire and the opening of the crossing points” between Gaza, Israel and Egypt, he said.
The leader of Israel’s opposition Likud Party, Benjamin Nentanyahu, said Tuesday that ultimately Hamas would have to be removed from Gaza and if the government chose to do so in this war, he would support it.
