TEL AVIV, Israel — With Israel agreeing to suspend its bombing of Lebanon for 48 hours, signs are emerging that Prime Minister Olmert’s war Cabinet is divided on what it would seek before it agrees to a final cease-fire and how to further prosecute the war on Hezbollah.

Israeli officials say the assessments of the damage to Hezbollah by the military’s intelligence analysts and the Jewish state’s spy service, Mossad, differ widely.

While the Israel Defense Force accentuates the fact that the Iran- and Syria-funded terrorist organization’s intelligence, political, and communications infrastructure in Beirut has been decimated, Mossad stresses that the air campaign and limited ground offensive so far have failed to diminish Hezbollah’s fighters or the stores of missiles that have been raining on northern Israel.

Last night, the State Department announced that Israel would agree to “cease aerial activity in southern Lebanon “for 48 hours to investigate the attacks on a residential building in Qana early yesterday morning that killed at least 50 people, no less than 37 of which were children. Israeli officials said the building was believed to be a regional command center for Hezbollah.

They also agreed to coordinate with the U.N. humanitarian relief missions to Lebanese civilians, but under the plan Jerusalem retains the right to strike at positions that continue to prepare attacks on northern Israel.

The deal was announced just two hours after Iraq’s leading Shiite cleric and an American ally, Ayatollah Ali Sistani, announced that Muslim nations would not forgive America if it did not engineer an immediate cease-fire.

The differing damage assessments among Israelis have resulted in both military and diplomatic consequences. Over the weekend, some Israeli officials floated the idea that the government would be prepared to accept a cease-fire even before Hezbollah was disarmed, a distinct change from the earlier war aim supported by both Israeli generals and Mr. Olmert, who promised to cripple the terrorist group.

While that leak was quickly dismissed by Saturday evening, when the air raids on Hezbollah positions resumed for another night, Israel’s willingness to accept a temporary cease-fire late last night suggests that diplomatic pressure from America to end the conflict is causing Mr. Olmert to bend at last.

A former chief of the IDF research and assessment division, Yaacov Amidror, said the primary rift in Mr. Olmert’s war Cabinet is between those who believed a limited military offensive would cripple the military wing of Hezbollah and those who did not.

“I am surprised by your surprise that seven Israelis sitting together would disagree,” Mr. Amidror said. “Here is the primary difference: Those who believe we will do the dirty job of fighting Hezbollah on the ground believe we should send the soldiers in. And then there are those who believe at the end of the day there is no way to end Hezbollah — those who think we are foolish to send them in now.

“I am between those who believe we can’t do it and those who think we can. I think it would make a huge difference to any international force if they did not have to deal with a fully armed and functional Hezbollah,” he said.

The ambivalence of the IDF so far to commit to a full ground campaign is perhaps most apparent in the IDF’s decision last week to announce its decision to call up 30,000 reserves while simultaneously stating it had no intention of taking its ground fight farther into Lebanon.

The decision to call up more reserves was followed Saturday by Israel’s decision to pull troops from Bint Jbeil, a Hezbollah stronghold and scene of some of the war’s heaviest fighting, which the IDF claimed to have been captured.

The former Likud chairman of the Knesset’s national security committee, Yuval Steinitz, said the air campaign against Hezbollah’s infrastructure has been successful. “Hezbollah suffered a heavy blow on its headquarters and elsewhere, lost most of its intelligence headquarters, and supply installation, and communication and training centers,” Mr. Steinitz, a subcommittee chairman of the national security committee who receives regular intelligence and military briefings on the war, said.

“Unlike Al Qaeda and Hamas, Hezbollah today is a state within a state, with very advanced training centers all over Lebanon,” he said. “They lost all of this. The only thing that remains is the fighting units and artillery in the south of Lebanon.”

Mr. Steinitz, who broke with former Prime Minister Sharon over his plan to disengage from Gaza, described the air campaign against the political and intelligence targets of Hezbollah as a “great success.” But he added that the ground campaign has not been so effective.

He said the mission will not be a success unless more ground troops are committed. “You cannot do it without occupying south Lebanon for at least a week or two. It goes without saying Israel should have captured southern Lebanon about a week ago.This is the first time in Israel’s history since 1948 that the country’s center, or almost the center, has come under such fire. They are shooting on Haifa on the Haifa Bay. Almost 2 million Israelis have had to move south or into defense shelters,” he said.

Messrs. Steinitz and Amidror both said that if the war were to stop today, it would be considered a victory for Hezbollah. “If there is a cease-fire now, there is no way to claim we won. It will be a victory for Hezbollah,” Mr. Amidror said. “The only thing to prevent this is to kill the other launches and clear southern Lebanon.”

But he added that the implementation of U.N. Security Council resolution 1559, which requires Hezbollah to disarm, would be a “strategic failure” for the militia. “Can this be implemented without killing too many civilians?” he asked. “This depends on the prime minister [Olmert] and the secretary of state [Rice] and what they are [negotiating] right now.”