Her statement came as AFP quoted a US source saying Secretary Rice would also fly into Lebanon by helicopter from the nearby island of Cyprus as part of the trip to discuss Israel's offensive on Lebanon.
"We believe a ceasefire is urgent. It is however important to have conditions that make it sustainable," Secretary Rice said en route to Israel.
AP reported that Secretary Rice also indicated an openness to working with Syria to resolve the crisis.
In recent weeks, the Bush administration has blamed Syria, along with Iran, for stoking the recent violence by encouraging Hezbollah to attack northern Israel.
"The problem isn't that people haven't talked to the Syrians. It's that the Syrians haven't acted," Secretary Rice said.
"It's not as if we don't have diplomatic relations," she said. "We do."
Secretary Rice and US President George W. Bush have rejected calls for an immediate ceasefire, saying Israel has a right to defend itself from terrorism and Hezbollah must return two captured Israeli soldiers and stop firing missiles and rockets into Israel.
Civilians have taken the brunt of the conflict that has cost up to 369 lives in Lebanon and 37 in Israel.
Israeli warplanes pounded south Lebanon in the early hours of today, wounding six people, including one child, at a Palestinian refugee camp in Tyre.
Calls for ceasefire
Earlier in Washington, Saudi Arabia's Foreign Minister Prince Saud al-Faisal requested an immediate ceasefire in talks with Mr Bush and Secretary Rice.
"We requested a ceasefire to allow for the cessation of hostilities that would allow ... Lebanon to establish sovereignty over the whole of its territory," the Saudi foreign minister told reporters after the meeting.
The US administration had so far refused to back calls for an immediate ceasefire, saying that the Islamist militia must first be reined-in before efforts to establish a permanent peace can be stepped up.
The prince said the White House talks focused on "the inability of Lebanon to exercise sovereignty over its territory. This is what we all agree is the primary concern of everybody."
The US is seeking to encourage friendly Arab states – including Saudi Arabia and Egypt - to pressure Syria to end its support for Hezbollah, which Washington blames for triggering the conflict.
Saudi officials said the prince would also propose an "exchange of prisoners" between Hezbollah and Israel, something the Israeli government has so far ruled out without the prior release of the two soldiers captured on July 12.
UN chief condemns Israel
Earlier today the United Nations humanitarian chief, Jan Egeland, condemned Israel for "violating humanitarian law" over its raids on Lebanon.
Mr Egeland, in Beirut to launch an urgent appeal for funds for half a million people made homeless by the conflict, toured bombed-out areas.
"This is destruction of block after block of mainly residential areas. I would say it seems to be an excessive use of force in an area with so many citizens," he told reporters in southern Beirut, a Hezbollah stronghold.
Asked if the Israeli raid constituted a war crime, he replied: "It makes it a violation of humanitarian law."
Israeli Justice Minister Haim Ramon said the aim of the offensive was to keep Hezbollah - which controls southern Lebanon in the absence of the regular Lebanese army - at least 20 kilometres from the frontier.
Israel, which has massed its troops on the border, seized control of the strategic hilltop village of Marun Al-Ras on Saturday after sending tanks, bulldozers and armoured cars across the border.
But Defence Minister Amir Peretz insisted Israel did not plan an all-out invasion. "The ground operation is focusing on a limited entry of forces," he told the cabinet. "We are not dealing with an invasion of Lebanon."
Syria warns
Meanwhile Syria, blamed by the US for stoking the conflict, warned that if Israel invaded Lebanon it would have no choice but to respond.
"If Israel makes a land entry into Lebanon, they can get to within 20 kilometres of Damascus," Information Minister Moshen Bilal told the Spanish newspaper ABC.
"What will we do? Stand by with our arms folded? Absolutely not. Without any doubt Syria will intervene in the conflict."
US ambassador to the United Nations John Bolton rebuffed a previous Syrian offer of dialogue saying that "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,” Mr Bolton said.
Lebanon's foreign minister Fawzi Salloukh meanwhile said the two Israeli soldiers captured by Hezbollah were apparently in good health.
He said his country is ready to start negotiating with an intermediary over a prisoner swap with Israel.
NATO force proposed
The US and Israel indicated on Sunday that they were ready to support an international force in south Lebanon led by NATO.
No US troops are likely to be in the force, which according to US media reports could be between 10,000 and 20,000 strong and led by a contingent from France or Turkey.
There could be delicate questions, however, over whether the force's mission is to disarm Hezbollah or to support the Lebanese army's efforts to take control in the south of the country.
Mr Bolton said the US administration would take the idea of NATO leading a buffer force "seriously".
In Jerusalem, Defence Minster Amir Peretz said Israel supported the deployment of an international force in southern Lebanon.
Lebanese Prime Minister Fuad Siniora said, however, that the UN should take the lead if an international force is to be established.
The Israeli defence minister discussed the idea during talks in Jerusalem with German Foreign Minister Frank-Walter Steinmeier.
British Prime Minister Tony Blair and other leaders have already called for a "robust" force, to take the place of the 2,000-strong UN observer mission already in Lebanon.
Israeli Prime Minister Ehud Olmert, whose army is also fighting a second offensive in the Gaza Strip, said he would accept a peacekeeping force in Lebanon "made up of troops from European Union countries".
Its mandate "will have to include control of the border crossings between Syria and Lebanon, deployment in south Lebanon and support for the Lebanese army," he said.
His comments came amid mounting international criticism of the Israeli offensive, which has left Lebanon virtually cut off from the world, made hundreds of thousands refugees in their own country and destroyed billions of dollars of infrastructure.
Even a minister from close US ally Britain, which had drawn Arab anger for appearing to back US support of the bombardment, has described Israel's tactics as "very difficult to understand".
Meanwhile Israel said it had opened an 80km by 8km safe passage to Beirut for ships and aircraft, a humanitarian corridor to allow aid to the Lebanese.
Israel's air and sea blockade put Lebanon's only international airport out of action, and the bombing of houses, roads, bridges, factories, warehouses and trucks has created scenes reminiscent of the 1975-1990 civil war.