Secretary of State Condoleezza Rice said Tuesday the time has come for a new Middle East and an urgent end to the violence hanging over the region.

"I have no doubt there are those who wish to strangle a democratic and sovereign Lebanon in its crib," Rice said. "We, of course, also urgently want to end the violence."

Standing beside Israeli Prime Minister Ehud Olmert as they prepared to meet in his office, Rice reiterated the United States position that a cessation of hostilities in Lebanon must come with conditions that make an enduring peace.

"It is time for a new Middle East," she said. "It is time to say to those that don't want a different kind of Middle East that we will prevail. They will not."

Olmert welcomed Rice warmly and vowed that "Israel is determined to carry on this fight against Hezbollah." He said his government "will not hesitate to take severe measures against those who are aiming thousands of rockets and missiles against innocent civilians for the sole purpose of killing them."

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Earlier in Beirut, Rice disappointed her Lebanese hosts by saying in a face-to-face visit that the U.S. would not press Israel for a quick cease-fire without addressing the longer-term threat from Hezbollah.

With little diplomatic progress to show for her lightning trip to Beirut early Monday, the Bush administration instead focused on the announcement of $30 million in humanitarian aid for Lebanon, which has borne the brunt of fighting between Israel and Hezbollah guerrillas.

Rice's visit marked the first high-level U.S. diplomatic mission to the area since fighting erupted on July 12, violence that has complicated hopes for peace and democracy in the region.

Lebanese leaders had hoped her trip would hasten a cease-fire in the fighting between Israel and the Hezbollah militants in Lebanon that has claimed hundreds of lives, mostly Lebanese civilians.

"Thank you for your courage and steadfastness," she told Prime Minister Fuad Saniora, who has repeatedly asked for international help in bringing a halt to cross-border Israeli-Hezbollah shelling. Rice flew next to Jerusalem but made clear that she would not pressure Israeli leaders for an immediate cease-fire during meetings Monday and Tuesday.

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"We're talking about the humanitarian situation, and we're also talking about a durable way to end the violence," Rice said before leaving Lebanon.

In a meeting that appeared tense, Saniora told the U.S. diplomat that Israel's bombardment had taken his country "backwards 50 years," the prime minister's office said. And Nabih Berri, a veteran Lebanese politician who is Lebanon's parliament speaker and Hezbollah's de facto negotiator, rejected proposals brought by Rice almost as soon as she left.

Berri told Rice that a cease-fire must precede any talks about resolving Hezbollah's presence in Lebanon, an official close to the speaker said. Rice, reflecting the U.S. view that a quick cease-fire would not be sustainable, had proposed that the fighting stop at the same time that an international force deployed in southern Lebanon, the official said. Rice also proposed that Hezbollah weapons be removed from a buffer zone extending about 18 miles from the Israeli border, said the official. He spoke on condition of anonymity because the talks were private.

Berri proposed instead a two-phased plan. First would come a cease-fire and negotiations for a prisoner swap. Then an inter-Lebanese dialogue would work out a solution to the situation in south Lebanon.

The Bush administration has said that a cease-fire would be premature unless it addresses the threat Hezbollah fighters pose to Israel.

Asked whether Rice's meeting with Berri went poorly, Assistant Secretary of State David Welch replied, "That's unfair." Welch added, however, that Berri approached the session with the position that a prisoner exchange would resolve other problems.

"That is not what we think," Welch said.

Underscoring the fragile security situation, Rice's car convoy whisked past armed Lebanese security guards as it shuttled across the battered capital. Though south Beirut has been heavily targeted by Israeli warplanes because of Hezbollah's presence there, no explosions were heard during her stay.

Rice said Bush wanted her to make Lebanon the first stop on her trip to the region. Her aides also sought to put a distinctly U.S. mark on diplomatic efforts. Yet she's offered no solutions publicly to end the violence and reach the long-term solution the U.S. is seeking.

"With this stop now, we — the United States — are firmly in the picture in leading the diplomacy, with the secretary of state doing that job," Welch said.

Rice's nearly two-hour meeting with Saniora went on longer than planned. She also met for about 45 minutes with Berri, who is considered friendly to Syria, which held political and military sway in Lebanon for decades before pulling out troops last year.

Going into the session at Berri's lavish office and residence, Rice said, "I am deeply concerned about the Lebanese people and what they are enduring. I am obviously concerned about the humanitarian situation."

Berri is an influential figure in Lebanon's complicated and factionalized political structure. Although the United States considers Hezbollah a terrorist group and has no direct dealings with it, Rice has met with Berri before. Rice could use her discussions with him to send an indirect message to Hezbollah, and to try applying pressure on Syria.

Rice also met with members of the Lebanese parliament who have been staunch opponents of Syria's influence in Lebanon. After visiting Israel, she was to fly to Rome, where she expects to meet with officials of European and moderate Arab governments.

Rice's five-hour visit to Beirut was not announced in advance because of concerns for her safety. She rode in a phalanx of SUVs through largely deserted streets patrolled by Lebanese Army troops.

Beirut, shattered during Lebanon's horrific civil war, has again become a war zone as Israel tries to extinguish what it calls the terrorist threat from Hezbollah militants.

American and other refugees have been streaming out of Beirut for more than a week. Israeli bombing has displaced an estimated half million people in Lebanon, and destroyed infrastructure worth an estimated $1 billion.

President Bush has ordered helicopters and ships to Lebanon to provide humanitarian aide, the White House announced.

Welch, the assistant secretary of state, said the U.S. was offering $30 million largely in goods, part of what was hoped would be a $100 million to $150 million U.N. aid package. He said the U.S. assistance would include medical kits for 100,000 people as well as 20,000 blankets.

"We are working with Israel and Lebanon to open up humanitarian corridors," Bush spokesman Tony Snow said at the White House.

Nearly 12,000 Americans have been evacuated over the past week, including more than 2,000 in the past 24 hours, said Pentagon spokesman Bryan Whitman.