A diplomatic team from Saudi Arabia met with President Bush and Secretary of State Condoleezza Rice on Sunday to press them to play a more influential role in the Middle East conflict by urging Israel to lay down its arms.

The meeting lasted just over an hour, and in it, Saudi Foreign Minister Saud al-Faisal, Saudi Ambassador to the United States Prince Turki al-Faisal and Saudi National Security Council chief Prince Bandar bin Sultan urged Bush to press for an immediate cease-fire in the Middle East.

"We requested a cease-fire to allow for the cessation of hostilities," the foreign minister said. He also handed a letter to Bush from Saudi King Abdullah asking for the United States to help intercede to get Israel to stop its bombing campaign.

A White House spokeswoman Eryn Witcher did not comment on any plan to seek a ceasefire, speaking only to the mutual concern about Lebanese civilians caught in the crossfire of Hezbollah and Israeli bombing.

"They discussed the shared goals of helping the people of Lebanon and restoring sovereignty to the government of Lebanon and building stronger Lebanese armed forces, deploying in all of Lebanon territory," Witcher said. "They also discussed the humanitarian situation, reconstruction and putting conditions in place that would put an end to violence."

After the Oval Office meeting, Rice headed to the region to meet with leaders from Israel and elsewhere.

Prior to it, Bush, who spent the weekend at his ranch in Crawford, Texas, had directed Rice to find ways for any end to violence to be sustainable. He had already said that any cease-fire that fails to incapacitate Hezbollah does not make diplomatic sense.

Saud al-Faisal said Bush wants an end to the the violence but did not reveal how Bush responded to the request.

"I found the president very conscious of the destruction and the bloodshed that the Lebanese are suffering," he said. "His commitment (is) to see the cessation of hostilities. I have heard that from him personally, and that is why he is sending Ms. Rice to work out the details."

The Saudi diplomats also denied a New York Times report that suggested that the administration is pushing behind the scenes for Saudi Arabia to reach out to Syria in an effort to convince it to turn against Hezbollah.

"There is only one problem with this crisis — that is Lebanon and the inability of the Lebanese to establish sovereignty over its territories. This is what we both agreed was the primary concern of everybody," the foreign minister told reporters outside the West Wing. "Everyone who needs to help and must help, should help."

Saud al-Faisal said he didn't want to tell any more details about the meeting so as not to prejudice Rice's trip. Rice is beginning her mission in Jerusalem, where she'll meet with Israeli Prime Minister Ehud Olmert. On Tuesday, she'll head to Ramallah in the West Bank for a meeting with Palestinian President Mahmoud Abbas.

"What we're trying to do here is put together the elements for a sustained solution to the problem, at least between Lebanon and Israel, to strengthen the government of Lebanon, to eliminate the Hezbollah terrorist threat which threatens both innocent civilians of Lebanon as well as Israel, and not to rush into anything precipitously," U.S. Ambassador to the United Nations John Bolton told "FOX News Sunday."

"The worst result here would be a partial solution that returns us to this kind of problem again in a matter of weeks or months. We've got to think of the longer term here. There may be an opportunity. We need to go about it in a sustained fashion," Bolton added.

Rice will not meet with the leaders of the terror group or its sponsor Syria despite a message Sunday morning from Syrian Deputy Foreign Minister Faisal Meqdad that said Damascus is ready for dialogue with the United States.

Bolton said such a meeting would serve no purpose.

"I mean 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," Bolton said.

On Wednesday, Rice heads to Rome where she'll meet with diplomats from Europe and moderate Arab nations. Neither Israeli nor Palestinian representatives will attend.

Also on the Rome agenda will be discussion on the extent of force being used in the Middle East and ways to shore up the Lebanese government, which right now cannot control Hezbollah.

"She'll be talking to friends and allies as to whether and when force is appropriate and how it should be constructed," White House Chief of Staff Josh Bolten said.

Among the options to be discussed is what kind of force can be put into the region when the fighting ends. Bolten said Sunday that international peacekeepers might be an option, but U.S. troop involvement was unlikely.

"Secretary Rice said she didn't consider it all that likely," Bolten told NBC's "Meet the Press," adding that Rice would discuss with allies whether and when force is appropriate, as well as what form it might take. As for an international operation, Bolten said, "Secretary Rice said we're open to that."

Israel's defense minister said Sunday that his country would accept a temporary international force, preferably headed by NATO, along the Lebanese border to keep Hezbollah guerrillas away from Israel, according to officials in the minister's office.

"We have been looking carefully at the possibility of a multinational force, perhaps authorized by the Security Council, but not a U.N.-helmeted force," Bolton said.

Bolton noted that a U.N. force has been present at the Israel-Lebanon border for decades without helping to institute peace.

"Well, the U.N. force that's there now really does not have the mandate to do it, and here's an interesting little fact. That force is called the U.N. Interim Force in Lebanon. It was sent there on an interim basis in 1978, 28 years ago. So it's been a long interim and I think, sadly, has not been successful," Bolton said.

The chairman of the Senate Foreign Relations Committee endorsed the idea of a NATO force, without U.S. soldiers.

"It would not a good idea for the United States troops to be in Lebanon," said Sen. Richard Lugar, R-Ind. "I don't say that in a qualified way. I just say this categorically. We're going to have troops there, I believe of one country or another, but not the United States of America. We are extended in the area."

Bolten said the U.S. will stand firmly behind Israel, noting that an attack on an ally is considered an attack on the U.S.

"We are allies, and we will support Israel in its right to self-defense," he said. "At the same time, we will do everything possible to make sure the crisis has a minimal impact on civilians."

The White House meeting with the Saudis follows visits to Washington last week by Egypt's intelligence chief and foreign minister, who met with Rice and Bush's national security adviser.

Bush says his administration's diplomatic efforts in the Mideast will focus on strategy for confronting Hezbollah and its supporters in Syria and Iran. In his radio address Saturday, the president said Syria has been Hezbollah's primary sponsor for years and helped provide shipments of Iranian weapons.

"Iran's regime has also repeatedly defied the international community with its ambition for nuclear weapons and aid to terrorist groups. Their actions threaten the entire Middle East and stand in the way of resolving the current crisis and bringing lasting peace to this troubled region," Bush said.

Visit FOXNews.com's Mideast Center for more in-depth coverage.