TEL AVIV, Israel — With Israeli tank divisions and soldiers amassing along the border with Lebanon, America’s top diplomat yesterday tried to persuade Prime Minister Olmert to call off an expanded ground invasion.

Secretary of State Rice made two phone calls to Mr. Olmert, according to the State Department. Israeli television reported that for one of the calls, Mr. Olmert was taken out of a Security Cabinet meeting on the expanded offensive. Two Bush administration officials told The New York Sun last night that Ms. Rice intended to get guarantees from the Israeli premier to call off the larger invasion as she prepared to go to New York and salvage a U.N. cease-fire resolution that now appears to be scuttled.

In public, the tone of the White House — which ordered the Pentagon to supply Israel with more bombs in the first days of the conflict — appeared to shift. Yesterday, the White press secretary, Tony Snow, warned against “escalations” on both sides. At the State Department, spokesman Sean McCormack said he was not in the habit of commenting on Israel’s military operations. But he did reiterate, “We have, in the past, very strongly counseled, both in public and private, that the Israeli government needs to take the utmost care to avoid any loss of innocent life.”

An Israeli official pointed out that the Security Cabinet yesterday “decided in principle to expand the operation, while holding out for a diplomatic solution through the Security Council resolution.” The official, who requested anonymity, pointed out that there has not been an “announcement of an expanded invasion.”

The differences behind the scenes between America, which is seeking to cobble together a cease-fire resolution and multinational force, and Israel, which appears now to be preparing at least three divisions for a wider invasion, may not be so great. Israeli military officials have insisted for two weeks that they would support a diplomatic solution creating a multinational force to serve as a buffer in southern Lebanon. As a result, until last night the fighting involved smaller operations in border towns.

A Likud member of the Knesset’s defense and foreign affairs committee who has supported a larger invasion, Yuval Steinitz, said he was not privy to the details of the conversation between Ms. Rice and Mr. Olmert. “I don’t know what she is saying, but this decision is up to Israel. We have to decide how to defend Galilee and Haifa,” he said.

[Yesterday was the deadliest day of the war for Israeli troops in Lebanon, with 15 soldiers killed, the Associated Press reported.The plan approved by Israel’s Security Cabinet to force Hezbollah guerrillas — and their short-range rockets — out of southern Lebanon and past the Litani River would escalate the fierce fighting and, if successful, leave Israel in control of a security zone that it evacuated six years ago after a bloody 18-year occupation.

A new Israeli offensive would also put tremendous pressure on the United Nations to agree quickly on a cease-fire to end the fighting that has killed at least 829 people, caused widespread destruction across southern Lebanon, and forced hundreds of thousands of Israelis into bomb shelters. Israeli officials implied they would halt the new offensive if a cease-fire agreement removes Hezbollah from the border.

A minister in Israel’s Security Cabinet said the offensive might not begin for two or three days to give more time to cease-fire talks, but senior military officials said the operation could begin very quickly.

Soon after the Cabinet decision, a column of Israeli tanks and armored vehicles crossed into southern Lebanon and took up positions inside Lebanese territory, witnesses said. The Litani River is about 18 miles north of the border.

Before the new offensive got off the ground, fighting intensified in the border strip that 10,000 Israeli troops were already occupying four miles into southern Lebanon.

Fifteen Israeli soldiers were killed in a single day of fighting yesterday, the military said, the highest one-day total in the Israel-Hezbollah conflict. The military said 38 soldiers were wounded in battles across south Lebanon.

Israel also hit Lebanon’s largest Palestinian Arab refugee camp with an airstrike, killing at least two people. Israeli attacks yesterday killed eight Lebanese civilians, according to Lebanese officials, and three guerrillas, according to Hezbollah.

An Israeli TV station, quoting unidentified sources, said Iranian Revolutionary Guard soldiers were among the Hezbollah dead. The Israeli military was unable to confirm the report. Israel has said Iran is aiding Hezbollah on the ground as well as supplying the guerrillas with weapons. Iran has denied the allegations.

Israeli warplanes also dropped leaflets over the southern port city of Tyre and over Beirut proper for the first time. The fliers criticized the Hezbollah leader, Sheik Hassan Nasrallah, saying he was “playing with fire” and that the Lebanese people were “paying the price.”

Hezbollah fired at least 170 rockets into Israel yesterday, the army said.

Since the fighting began, at least 711 people have died on the Lebanese side of the conflict. The Israeli death toll stood at 118, including 36 civilians and 82 soldiers.

Israel’s Security Cabinet was told a new offensive could mean 100 to 200 more military deaths, according to a participant. Military officials said it would take the army several days to reach the Litani and then several more weeks to rid that area of Hezbollah’s fighters and rocket launchers.

“The assessment is [the new offensive] will last 30 days,” Trade Minister Eli Yishai, a member of the Security Cabinet who abstained from the vote, said. “I think it will take a lot longer.”

The offensive was expected to eliminate 70% to 80% of Hezbollah’s short-range rocket launchers, senior military officials said.

The offensive was approved 9–0, with three abstentions at an intense six-hour meeting.The government’s decision came two days after Lebanon offered to send 15,000 soldiers to patrol the border region, a key Israeli demand intended to prevent attacks on Israel. The current fighting began when Hezbollah fighters crossed into Israel on July 12, killing three soldiers and capturing two others.

In a major shift, Sheik Nasrallah said Hezbollah supported a deployment by the Lebanese army after a cease-fire is declared and Israel leaves.

Israeli officials remained skeptical of the Lebanese offer and were not convinced Lebanon’s army would take concrete action to stop Hezbollah attacks.

“It is important that the Lebanese army will be accompanied by an international force that will enable it to reach the south in an organized manner, and to leave the place clean of Hezbollah,” Foreign Minister Tzipi Livni said.

Some soldiers said Israel was having trouble controlling even the small strip it was already occupying.

“The biggest problem is still the existence of Hezbollah fighters all over the place, even though we have most of the territory under control,” an officer in a reserve brigade in southwestern Lebanon, Major Avi Ortal, said.

“Hezbollah are good fighters. They know the territory. They live there and they have had six years to build compounds,” he said.]