The Lebanese government announcement says Rice arrived in Beirut Monday and is expected to meet with Prime Minister Fuad Saniora before she traveling to Israel, her originally announced destination.
As fierce fighting continues in the 13-day-old war Israel and the Lebanon-based Islamic militia Hezbollah, diplomats have been exchanging offers of peace, warnings and threats.
Saudi Arabia Sunday asked President Bush to intervene in Israel's military campaign against Hezbollah in Lebanon to stop the mounting deaths.
"We are requesting a cease fire to allow for a cessation of hostilities," Saudi Foreign Minister Prince Saud al-Faisal said after an Oval Office meeting with Mr. Bush.
Saud said he gave the president a letter from Saudi King Abdullah asking that Mr. Bush help seek an immediate cease fire in the Middle East conflict.
Rice also participated in the meeting before departing for Israel in the first U.S. diplomatic effort on the ground since Israel began bombing Lebanon.
"We believe that a cease fire is urgent," Rice said early Monday, commenting during a refueling stop at Shannon Airport in Ireland on her way to the Mideast. "It is important, however, to have conditions that will make it sustainable."
Rice says she has been consulting with the United Nations and Israeli officials about possible elements of a cease fire agreement that could ensure Lebanon has control of its country.
The U.S. Secretary of State dismissed critics who say the U.S. should talk directly to Syria - which has been accused of supplying weapons to Hezbollah, the militant group at war with Israel - to bring about peace in the region. She noted that the U.S. does have a mission in Damascus through which the U.S. can talk to the Syrian government, but she said those attempts have been futile in the past.
"Let's remember we talked to the Syrians over and over and over again. Colin Powell talked to the Syrians, [former deputy secretary of state and current ConocoPhillips board member] Rich Armitage talked to the Syrians," said Rice. "The problem isn't people haven't talked to the Syrians – it's that the Syrians haven't acted."
Rice insisted "plenty of people" have been sending messages to the Syria to stop supporting terrorism and "not to meddle in the affairs of Lebanon."
She told reporters she wasn't sure if Syria and Iran have any misgivings about supporting Hezbollah, but said: "I would think if they want good relations, they might start by ending their support in those ways."
Syria has said that it will press for a cease fire, but only in the framework of a broader Mideast peace initiative.
In other recent developments:
"She will be talking with our friends and allies about whether and when a force is appropriate and how it might be constructed," said White House Chief of Staff Josh Bolten.
"Rice's trip illustrates the need for the U.S. to be involved in a comprehensive Middle East peace effort that is shaped around the framework established by the U.N. in Resolution 1559 - passed by the world powers two years ago - which called for the disarming of Hezbollah," says CBS Foreign Affairs Analyst Pamela Falk. "The Security Council meeting at the U.N. this past week underscored the need to make certain that her trip involves the moderate Arab states in the mediation efforts to keep Syria from rearming militias in the region."
"Syria and Spain are working to achieve a cease fire, a prisoners' swap and to start a peace process as one package," Syrian Information Minister Mohsen Bilal told the Spanish daily newspaper ABC during an interview in Madrid.
"What we are calling for is de-escalation, diplomatic engagement and for the United States to restart playing the role it used to play in the past, the role of the broker of peace," Dr. Imad Moustapha, the Syrian ambassador in Washington, said on CBS's Face The Nation.
But U.S. Ambassador to the United Nations John Bolton said Syria "doesn't need dialogue to know what they need to do. They need to lean on Hezbollah to get them to release the two captured Israeli soldiers and stop the launch of rockets against innocent Israeli civilians."
"Syria, along with Iran, is really part of the problem because of their longtime support for Hezbollah and other armed groups inside Lebanon," Bolton told "Fox News Sunday." "So I don't know what that adds necessarily, although I suppose it's better than nothing."
"We support Hezbollah because Hezbollah is a national liberation movement," Moustapha told Bob Schieffer. "Everybody should understand that the issue in the Middle East, the true issue is the ongoing Israeli occupation of our territories."
It is unlikely that Israel would agree to Syria's conditions, but the remarks were the first indication of Syria's willingness to be involved in international efforts to defuse the Lebanese crisis. The offer also came with a warning.
"If Israel invades Lebanon and enters it by land, then it will be only about 12 miles from Damascus, then we will not stand with our hands tied," Bilal said.
Iranian President Mahmoud Ahmadinejad said Israel had "pushed the button of its own destruction" by attacking Iranian-backed Hezbollah in Lebanon.
He didn't elaborate, but suggested Islamic nations and others could somehow isolate Israel and its main backers led by the United States.
Israeli Defense Minister Amir Peretz met with German Foreign Minister Frank-Walter Steinmeier, one of a series of diplomatic meetings aimed at ending the fighting. French Foreign Minister Philippe Douste-Blazy was also in Israel. On a tour of Haifa, Douste-Blazy was chased into a stairwell by air-raid sirens and incoming missiles.
"The goal is to create a situation in which we have as broad a space for diplomatic movement as possible," Peretz said after meeting Steinmeier. "The goals we set for ourselves will be achieved. We certainly see a combination of a military operation that is fulfilling its role plus broad international activity to complete the process."
Israel said it would accept a NATO-led international force to keep the peace along the border.
"We would like to see an effective force, which has some capabilities to defend itself, and, also, to bring law and order," Daniel Ayalon, the Israeli Ambassador in Washington, said on Face The Nation.