Ahead of a visit to the Middle East, President Bush expressed some optimism that an Israeli-Palestinian peace agreement would be struck before his term ends while holding out little hope for a major breakthrough when he arrives in Israel on Wednesday.

Secretary of State Condoleezza Rice said Tuesday reaching such a deal within the next eight months "might be improbable but it's not impossible."

Bush left the White House late Tuesday afternoon on the trip that will first take him to attend ceremonies in Jerusalem marking the 60th anniversary of the founding of the Jewish state. He also will go to Saudi Arabia where he promises to press King Abdullah to increase oil production to ease soaring costs on consumers. Bush made a similar plea in January but it was ignored.

As Bush prepared to leave Washington, Senate Democrats introduced a resolution that would block $1.4 billion in arms sales to Saudi Arabia unless Riyadh agrees to increase its oil production by 1 million barrels per day.

The Democrats said they introduced the measure to coincide with Bush's trip to send a message to Saudi Arabia that it should pump more oil to reduce the cost of gas for Americans.

"We are saying to the Saudis, If you aren't helping us, why should we be helping you?" said Sen. Charles Schumer, D-N.Y.

The move might be largely symbolic. Congress usually has 30 days to block international arms deals once notified by the administration, and all of the sales in question were announced long ago. Still, Schumer said that Congress still has the right to intervene because the weapons have not been delivered.

The president's final stop will be at the Red Sea resort of Sharm el-Sheikh, where he will meet over two days with a handful of leaders: Egyptian President Hosni Mubarak, Afghan President Hamid Karzai, Palestinian Authority President Mahmoud Abbas and Prime Minister Salam Fayyad, Jordan's King Abdullah II and Iraqi leaders. Bush also is scheduled to meet with Lebanese Prime Minister Fuad Saniora, but that is in doubt now after clashes between the U.S.-backed government in Beirut and Hezbollah-led opposition.

In an interview on Tuesday with Politico and Yahoo News, Bush said that while a grand peace between Israel and the Palestinians "looks distant" at this point, "the big challenge in the 21st century is to advance freedom in the Middle East, for our security."

"Americans at home ought to care for the advance of free societies throughout the Middle East," he said. "After all, this is the center of anti-Americanism and hatred."

He also criticized former President Carter's recent approach to the Middle East, suggesting it was one of "blame Israel for every problem."

Bush, in an earlier interview with BBC Arabic, said he was still optimistic that his goal of a peace agreement before he leaves office in January 2009 was obtainable.

"I think we can, I really do," Bush said. "We're going to work hard for that end. Look, it's hard, I understand that."

In a separate interview with the Israeli newspaper Haaretz, Bush said the United States cannot impose peace in the Middle East.

"I will come not as somebody who demands, but somebody who encourages," Bush said. He said, "I'm not running for the Nobel Peace Prize; I'm just trying to be a guy to use the influence of the United States to move the process along."

Bush said the peace negotiations would not be derailed by the corruption probe of Israeli Prime Minister Ehud Olmert, the fifth investigation into his conduct since he became prime minister two years ago. Olmert has said he will resign if indicted.

"This is not an Olmert plan; this is a plan of a government," Bush told Haaretz.

"It's a legal matter inside the system; the system will deal with it. ... And having said that, my relations with the prime minister have been nothing but excellent," Bush said. "I found him to be an honest guy. He loves his family, he's easy to talk to, he's a strategic thinker. And so we'll see what happens."

Negotiations between Israeli and Palestinian officials are being conducted in secret.

Rice said it was "a misperception that not that much is going on in the political negotiations." Her language was tempered, however.

"I'm also a big believer that nothing is really impossible," she said in an interview conducted Monday and aired Tuesday on CBS' "The Early Show." "It might be improbable but it's not impossible."

Speaking to reporters on Air Force One, National Security Adviser Stephen Hadley suggested that Bush might acknowledge the Palestinian role when marking the Jewish state's birthday. "We are going to Israel to celebrate the 60th anniversary of the founding of the state of Israel, and that is a great event," he said. "We also recognize that resulted in hardship for many Palestinian people."

White House press secretary Dana Perino said Tuesday that the two sides "have been doing a lot of good work behind the scenes, out of the glare of the spotlight and away from the microphones, which has helped them make some halting progress."

"It's sluggish, that's true," she said. "They have very complex issues to deal with, with decades of conflict that have built up. And if this was easy, it would have been solved a long time ago."

Echoing Rice, Perino said, "I would put it this way ... while it's exceedingly difficult, it's not impossible." She said the U.S. did not anticipate any major breakthroughs this week but that Bush believes his one-on-one meetings are the best way to make progress.

On Lebanon, Hadley said that Rice will be seeking to rally international support for the U.S.-backed government in the coming days after recent clashes with Hezbollah-led opposition. Bush and Saudi Foreign Minister Prince Saud al-Faisal have accused Iran of exacerbating the situation by supporting Hezbollah.

"Obviously, we are also going to talk to various countries about additional pressure that can be put on Syria and Iran because in our view they are what is behind this," said Hadley, indicating that a starting point might be the coming U.N. Security Council meeting in New York. "There is obviously more to do."

Regarding the possibility of more sanctions, Deputy National Security Adviser Elliott Abrams said: "We'll see what happens in New York."