Ahead of a visit to the Middle East, US President George W. 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.

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

Rice said it was "a misperception that not that much is going on in the political negotiations." The secretary of state's 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."

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 Jimmy 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."

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 US did not anticipate any major breakthroughs this week but that Bush believes his one-on-one meetings are the best way to make progress.