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Speaking in Cairo last week, President Obama repeated the declaration he first made in Turkey in April: "In Ankara, I made clear that America is not -- and never will be -- at war with Islam." Does the American public agree? Overall, it does. In a CNN poll taken last month by Opinion Research, just over one-third of Americans (36 percent) said they believe that the United States is at war with the Muslim world, while 62 percent rejected that idea.

But the poll revealed a bigger problem: 62 percent of Americans believe that the Muslim world considers itself at war with the U.S. That may explain the deteriorating image of Muslim countries in the eyes of Americans. In March 2002 -- six months after the 9/11 attacks -- 41 percent of Americans had a negative opinion of Muslim countries. Now it's 46 percent. That is more than double the number with a positive opinion (21 percent).

Obama is trying to repair the relationship. In Saudi Arabia last week, the president said, "I thought it was very important to come to the place where Islam began." Obama believes he has special standing to seek reconciliation. "I have known Islam on three continents," he said in Cairo, where he drew attention to the fact that "an African-American with the name Barack Hussein Obama could be elected president."

The president had competition. A voice recording attributed to Osama bin Laden criticized Obama for the first time and accused him of "walking the same road as his predecessors to build enmity among Muslims." Do Muslims see Obama as different? To some extent, they do. "This president provides hope," King Abdullah of Jordan said during his recent U.S. visit. "There is a new America."

In February and March, the Gallup Poll asked citizens of 11 Arab countries to assess the job performance of U.S. leaders. In eight of those countries, opinion was more positive than last year, when George W. Bush was president. Egypt was one of them. A year ago, only 6 percent of Egyptians had a positive view of U.S. leaders. Now it's up to 25 percent. An improvement, although far from a majority.

It's the same story in Saudi Arabia. In 2008, 12 percent of Saudis expressed a positive opinion of U.S. leaders. With Obama in the White House, 29 percent have a favorable opinion. Still, considerable numbers of Arabs appear to be reserving judgment about the new U.S. president. In many countries, the number of respondents answering "don't know" more than doubled.

Obama tried to be honest about the clash of interests between the United States and Muslim countries over the Middle East peace issue. He called America's bond with Israel "unbreakable" and said, "Privately, many Muslims recognize that Israel will not go away."

At the same time, Obama was the first president to speak about "Palestine" as an entity ("Israel's interest, Palestine's interest"). And he went further than previous presidents in calling for a freeze on Israeli settlement growth in the West Bank. That puts Israel's new prime minister, Benjamin Netanyahu, in a bind. If Netanyahu agrees to stop all settlement expansion, most Israelis would support him, according to a poll taken by the Israeli newspaper Yediot Achronot. But his right-wing coalition could fall apart. Meanwhile, Israeli opposition leader Tzipi Livni has accused Netanyahu of endangering U.S. support for Israel by refusing to endorse the idea of a Palestinian state.

In a few Arab countries polled by Gallup, opinion of the United States has turned more negative. The Palestinian territories was one. Lebanon was another. A victory by the Hezbollah-backed alliance in the Lebanese election on Sunday could have delivered a stinging rebuke to Obama just three days after he spoke in Cairo. But the initial results indicate a narrow victory for the Western-backed Lebanese government.

Democracy is risky. Obama has not made it the centerpiece of his foreign policy the way the Bush administration did. In his Cairo speech, Obama talked about the more universal theme of human rights, arguing that "governments that protect those rights are ultimately more stable, successful, and secure."