Ms Rice offered sympathy for the Israeli people as fighting raged between their armed forces and Hezbollah, on the eve of her talks with Prime Minister Ehud Olmert and Palestinian leader Mahmoud Abbas.
"This is a difficult time for the Israeli people, it is a difficult time for the Lebanese people, it is a difficult time for the Palestinian people," Secretary Rice said.
She also stressed the US position that a peace deal to end the Israeli conflict with Hezbollah would need to address what the US sees as the root cause of the crisis.
"Any peace is going to have to be based on enduring principles and not on temporary solutions," she said.
Washington is arguing that UN resolution 1559 and the Taif Agreement which ended Lebanon’s civil war in 1990 need to be fulfilled.
Both documents called for the Lebanese government to exercise full control over its territory and the disarmament of militias.
The US also accuses Syria and Iran of sponsoring Hezbollah, the group that sparked the current crisis by abducting two Israeli soldiers.
Ms Livni described Ms Rice's arrival in Jerusalem as "a very important visit."
"The free world is facing a threat, the goal of Hezbollah is to set the world aflame and we will not let them succeed," she said.
"There is no conflict between the people of Israel and the people of Lebanon, but Israel has no higher responsibility to protect its citizens."
Secretary Rice had earlier said she wanted an "urgent ceasefire" in the fighting between Israel and Hezbollah, but insisted it should be sustainable.
The battle has so far killed 373 people in Lebanon - most of them civilians - and 40 Israelis, as least half of them also civilians.
Earlier in Beirut Ms Rice said she was "deeply concerned" about the Lebanese people.
"Thank you for your courage and your steadfastness," she said as she began talks with Lebanese Prime Minister Fouad Siniora and Foreign Minister Fawzi Sallukh, a Hezbollah ally.
"I am deeply concerned about the Lebanese people and what they are enduring. I am obviously concerned about the humanitarian situation," Ms Rice said after talks with Mr Siniora.
Discord over 'ceasefire plan'
But Lebanese parliamentary speaker Nabih Berri appeared to reject a ceasefire proposal, an aide to the Lebanese official said.
A meeting between Ms Rice and Mr Berri, who is acting as an intermediary for the Shiite Muslim Hezbollah group, was marked by "differences," a un-named source close to Mr Berri said after Ms Rice’s visit.
"There was no agreement because Rice insisted on a mechanism on a global settlement before a ceasefire," the source said on condition of anonymity.
"Rice set, as conditions for a ceasefire, the withdrawal of Hezbollah to the Litani river and the deployment of an international force in the area which would, she said, allow the return of displaced people."
The Litani river is about 20km from the border with Israel, marking an area that is largely under the control of Hezbollah.
Mr Berri, a veteran Shiite politician, had called for a ceasefire to be followed by a prisoner exchange and for Israel to allow the return of Lebanese who had fled the south "before discussing a complete plan to resolve the conflict."
But Ms Rice had refused to discuss an exchange of prisoners, the source said.
Hezbollah has demanded the release of Arab prisoners held in Israeli jails in return for two soldiers it captured in a deadly border raid on July 12.
In an earlier meeting, Lebanese Prime Minister Fuad Siniora angrily attacked Israel for its relentless bombing campaign.
"Israeli aggression is not only targeting Hezbollah but Lebanon itself, sending it back 50 years with its bombardment," he told Ms Rice.
Siniora to consider plan
But later, The Washington Post reported the Lebanese Prime Minister Fuad Siniora had promised to consider with other members of his government Secretary Rice's plan.
Lebanese and US officials quoted by the newspaper said the plan called for the deployment of an international force, possibly led by the North Atlantic Treaty Organizatrion, in a buffer zone inside Lebanon for 60 to 90 days.
The international force would after that time would begin training the Lebanese army to disarm and control Hezbollah, the officials said.
"We came away convinced that Siniora and the US are on the same page, working toward the same ends," a US official travelling with Secretary Rice said.
Aid package unveiled
Soon after Condoleezza Rice left Beirut the US announced a US$30 million (A$40 million) immediate aid package for Lebanon.
Officials said US forces would start an airlift of 100,000 medical kits, 2,000 plastic sheets and 20,000 blankets on Tuesday.
"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," Assistant Secretary of State David Welch told reporters travelling with Ms Rice.
Secretary Rice heard from parliamentarians and government officials from many sectors of Lebanon's society that the country was on the verge of a bitter humanitarian crisis.
"The US has turned around and come up with a significant amount of funding," Mr Welch said, and would be contributing to a UN appeal for US$150 million in aid to help 800,000 made homeless by Israel's offensive against Hezbollah.
It was Ms Rice's first visit to the Middle East since the fighting on the Israel-Lebanon border erupted on July 12 when Hezbollah killed three Israeli soldiers and seized two others.
Washington has come under increasing pressure for bold action amid criticism it is stalling to allow Israel time to attempt to wipe out the Syrian and Iranian-backed Hezbollah.
On Wednesday Ms Rice is due to attend an international conference on Lebanon in Rome.