The Bush administration is not yielding to international calls for a prompt cease-fire to end Israel's devastating campaign against Hezbollah militia in Lebanon.

Instead, Secretary of State Condoleezza Rice is trying to drum up diplomatic support for what on Tuesday she called a cease-fire of "lasting value." That is, one that would have the Lebanese army take over the south of the country where Hezbollah guerrillas have conducted a cross-border war against Israel for years.

"The Middle East has been through too many spasms of violence and we have to deal with underlying conditions," Rice said at a news conference.

Rice was meeting with President Bush early Wednesday afternoon to discuss her upcoming trip to the region, said White House spokeswoman Dana Perino. Perino said she had no information on Rice's itinerary.

Israel, in the meantime, is predicting its offensive could last for weeks, even as Lebanese and Israeli casualties mount. The Israeli military said early Wednesday it had sent some troops into southern Lebanon searching for tunnels and weapons.

On a familiar note, Bush pointed a finger at Syria, saying he suspects it was trying to reassert influence in Lebanon more than a year after withdrawing its troops under U.N. pressure.

"It's in our interest for Syria to stay out of Lebanon and for this government to survive," Bush said, referring to Prime Minister Fuad Saniora's fledgling government.

"Syria's trying to get back into Lebanon, it looks like, seems to me," the president said. "The world must deal with Hezbollah, with Syria and to continue to isolate Iran."

Rice has conferred by telephone with Israeli Prime Minister Ehud Olmert and Javier Solana, the senior European diplomat, and at the State Department with Foreign Minister Ahmed Aboul Gheit of Egypt, whose government is at the head of a moderate bloc of Arab nations.

She is likely to make a trip to the area this weekend, but there has been no announcement. State Department spokesman Sean McCormack said Wednesday she had not yet fixed a date. "She wants to time it so that it is useful and helpful in getting a cease-fire that is lasting and brings a durable cessation to violence," he said.

One of Rice's goals is creation of a peacekeeping force that would move into the region to keep the belligerents apart.

The administration has not be swayed by calls from Arab nations and moves at the U.N. Security Council for an immediate cease-fire. Asked Tuesday how long it might take to establish a foundation for a lasting cease-fire, Rice declined to offer an estimate.

A cease-fire should come "as soon as possible when conditions are conducive to do so," Rice said following her meeting with Gheit, who disagreed with her.

"A cease-fire is imperative," the Egyptian envoy said. "We have to bring it to an end as soon as possible."

Syria long has been suspected of funneling Iranian weapons to Hezbollah. In the recent fighting, the militia, which is committed to Israel's destruction, has used more potent missiles to reach deeper into Israel than ever before.

But Syrian deputy foreign minister Fayssal Mekdad denied Tuesday that his country was arming Hezbollah. "We have stopped all these kinds of things long time ago," Mekdad told CBS News.

On Capitol Hill, the Senate passed a resolution by voice vote Tuesday that supported Israel and said the chamber "holds the governments of Syria and Iran responsible for the acts of aggression carried out by Hezbollah and Hamas against Israel." The House was expected to pass a similar resolution Wednesday.

Bush reiterated his stance that Israel should be able to respond to attacks.

"We have made it very clear that Israel should be allowed to defend herself," the president said. "We've asked that as she does so that she be mindful of the Saniora government. It's very important that this government in Lebanon succeed and survive."

Bush spoke at the White House after briefing members of Congress about his trip to Russia for an economic summit that was overshadowed by fighting between Israel and the Islamic militant group Hezbollah.

"Everybody abhors the loss of innocent life," Bush told reporters. "On the other hand, what we recognize is that the root cause of the problem is Hezbollah. And that problem must be addressed ... by making it clear to Syria that they've got to stop their support to Hezbollah."

Later, Bush spoke by telephone with King Abdullah of Saudi Arabia, who expressed concern about the humanitarian situation in Lebanon, said a White House official who spoke anonymously because he was not authorized to make announcements.

Sen. Joseph Biden, D-Del., said he agreed with Bush that the United States should pressure Hezbollah, Syria and Iran.

"I think the president has an opportunity here to turn — as an old phrase goes — lemons into lemonade," Biden said, adding that some of Lebanon's Arab neighbors were siding publicly with the United States and Europe against Hezbollah.

Former House Speaker Newt Gingrich, a Republican, on Wednesday compared Hezbollah's actions with those of Germany's Adolf Hitler in the runup to World War II. "We didn't say 'let's negotiate with Adolf Hitler,"' Gingrich said on NBC's "Today" show. "We said Hitler's regime was evil, we had to have total victory."

Negotiating with Hezbollah, he said, would be wrong. "This is, in fact, a real war and the first stage has to be victory over Hezbollah, not a cease-fire," Gingrich said.