But in a tense, sometimes stormy debate that went on for nearly an hour, Secretary of State Condoleezza Rice dug in, and prevailed.Later, she defended the United States’ refusal to call for an immediate cease-fire, saying: “It doesn’t do anyone any good to raise false hopes about something that’s not going to happen. It’s not going to happen. I did say to the group, ‘When will we learn?’ The fields of the Middle East are littered with broken cease-fires.”

She said she expected that the issue would end up being resolved by the United Nations Security Council.

In a news conference after the talks, the normally placid Mr. Annan, made no effort to control his rage at Israel for what he had called an “apparently deliberate targeting” of a United Nations observer post in southern Lebanon by Israel on Tuesday. The attack killed four United Nations observers.

“Mr. Olmert definitely believes it was a mistake,” said Mr. Annan, referring to Israel’s prime minister, Ehud Olmert. But despite at least 10 calls from United Nations personnel to Israel that their positions were being shelled, Mr. Annan added, “The shelling of the U.N. positions began early in the morning and carried on all day.”

He pledged a formal investigation.

Ms. Rice and Mr. Annan disagreed at the news conference on whether Syria and Iran should be brought into the effort to end the violence. Mr. Annan called for working “with the countries of the region to find a solution,” naming Iran and Syria as players. Ms. Rice, by contrast, said she was concerned about Iran’s role and called on Syria to live up to its responsibilities, a reference to previous United Nations resolutions.

While the world has focused on the fighting in Lebanon, Israel has continued to shell Gaza. Most of those killed in Gaza on Wednesday were militants, but a mother and her two young daughters died when an artillery shell hit their home, the Palestinian Health Ministry said. A third young girl was also killed, and dozens of Palestinians were wounded.