"Any peace is going to have to be based on enduring principles and not on temporary solutions," the US secretary of state said after meeting Tzipi Livni, Israel's foreign minister, in Jerusalem.
Rice offered sympathy for the Israeli people as fighting raged between their armed forces and the Shia group, Hezbollah, on the eve of her talks with Ehud Olmert, the Israeli prime minister, and Mahmud Abbas, the Palestinian president.
Washington is arguing that UN resolution 1559 and the Taif Agreement, which ended the Lebanese civil war in 1990, need to be fulfilled.
Both documents call for the Lebanese government to exercise full control over its territory, and the disarmament of militias -including Hezbollah.
The United States also accuses Syria and Iran of sponsoring Hezbollah, which Washington considers a terrorist group.
Livni said: "The free world is facing a threat, the goal of Hezbollah is to set the world aflame and we will not let them succeed.
"There is no conflict between the people of Israel and the people of Lebanon, but Israel has no higher responsibility than to protect its citizens."
Tense talks in Beirut
there could be no ceasefire until Hezbollah released the two Israeli soldiers it captured on July 12.
A few hours earlier, Rice was in Beirut, where she told Fouad Siniora, the Lebanese prime minister, that
The tone of the meeting between
Rice and Siniora was "negative"
A Lebanese source quoted Rice as saying that the pair would have to be released unconditionally and Hezbollah forces moved about 20km from the border.
"The tone of the meeting was very negative," the source said.
Siniora has repeatedly called for a ceasefire since fighting began 13 days ago.
He has said only a broad political deal - including a prisoner swap and an Israeli withdrawal from the disputed Shebaa Farms area - will work.
Later during her visit, Rice told Nabh Berri, the Lebanese parliament speaker, that a ceasefire must be part of a deal that includes Hezbollah's withdrawal beyond the Litani River, 20km north of Israel, and the deployment of an international force in the border region.
She told Berri: "The situation on the border cannot return to what it was before July 12", referring to the day Hezbollah seized two Israeli soldiers during a raid into Israel, sparking a war in which 400 people have died on both sides, most of them Lebanese civilians.
Berri, a Shia close to Hezbollah said that there should be a sequence of events, "ceasefire, exchange of prisoners, and then discussing all other matters", a Lebanese source said.
US aid for Lebanon
David Welch, the US assistant secretary of state, who is travelling with Rice, said his country would "contribute $30 million" in humanitarian assistance to Lebanon.
"We knew this when we came in, but the immediacy of being in Beirut makes it very, very clear, there are some serious humanitarian problems"
David Welch, the US assistant secretary of state
The US aid package comes on the heels of a UN appeal for $150 million to help 800,000 Lebanese citizens made homeless by Israel's offensive.
"We knew this when we came in, but the immediacy of being in Beirut makes it very, very clear, there are some serious humanitarian problems," Welch said.
Rice had told reporters while in Beirut: "I am deeply concerned about the Lebanese people and what they are enduring."
On Wednesday, Rice will go to Rome to discuss the situation with European and Arab foreign ministers.
Kofi Annan, the United Nations secretary-general, said that he would press for a truce and the establishment of an international peacekeeping force at the meeting.
Israel has dropped its objections to the force and several European Union nations have said they will contribute troops, but EU officials also said that questions remained over how it could fulfil its mission.
Britain has backed the use of an international force as a "buffer" between Hezbollah and Israel.
But the prime minister has been under political pressure in Britain for joining President Bush in not publicly calling for an immediate ceasefire.
Although Tony Blair has been one of the prime backers of an international force, Britain is unlikely to contribute to one because of military commitments in Iraq and Afghanistan.
Britain has already committed its
troops in Iraq and Afghanistan
Nato reacted cautiously to calls for it to lead the peacekeeping force and diplomats pointed out that the military alliance was already hugely stretched, notably in Afghanistan.
"There are huge challenges involved for any kind of intervention force," one Nato source in Brussels said.
Nato in theory has the command structure, planning capability and political co-ordination capability to run a multinational operation, the source said.
But he said: "What [Nato] allies are willing to put at its disposal is a different question."
The Washington Post reported that France and Turkey could provide a significant number of troops, but Nato sources said getting enough fire-power would be a "huge challenge".