"The United States and Saudi Arabia have a long history of friendship. We have a strategic relationship," Mr. Obama said on the eve of his address to the Muslim world from Egypt.
During the first stop on his five-day trip through the Middle East and Europe, President Obama and Abdullah drank Arabic coffee and chatted briefly in public before holding private talks at the king's horse farm.
President Obama called the king wise and gracious, adding: "I am confident that working together that the United States and Saudi Arabia can make progress on a whole host of issues of mutual interest."
Abdullah in turn expressed his "best wishes to the friendly American people who are represented by a distinguished man who deserves to be in this position."
Just before departing for the Middle East, Mr. Obama spoke with the BBC about the need to open a new dialogue in this region of the world.
"You know, there are misapprehensions about the West, on the part of the Muslim world," President Obama said. "And, obviously, there are some big misapprehensions about the Muslim world when it comes to those of us in the West."
In Riyadh Wednesday, the president met with King Abdullah about a range of issues, including Iran's nuclear program, spikes in oil prices and Arab-Israeli peace efforts.
Throughout his trip, Mr. Obama is expected to press for Arab leaders to offer a gesture to Israel that might accelerate the peace process, the New York Times reported.
But political experts say such a gesture is unlikely.
"What do you expect the Arabs to give without getting anything in advance, if Israel is still hesitating to accept the idea of two states in itself?" Mohammad Abdullah al-Zulfa, a member of the Saudi Shura Council, which serves as an advisory panel in place of a parliament, told the Times.
Thursday's speech in Cairo, which will fulfill a campaign promise the president made last year to deliver an address from a Muslim capital early in his administration, is aimed at changing the tone of relations but Obama has cautioned that it is just the first step in finding common ground.
"I am confident that we're in a moment where in Islamic countries, I think there's a recognition that the path of extremism is not actually going to deliver a better life for people," Mr. Obama told NBC News before he left on his trip.
"I think there's a recognition that simply being anti-American is not going to solve their problems. The steps we're taking now to leave Iraq takes that issue and diffuses it a little bit."
President Obama's 2010 budget proposal seeks $86 million for the Middle East Partnership Initiative, a program developed in 2002 that promotes training of government officials, entrepreneurs, and activists, the Boston Globe reported. That would raise the program from $50 million in 2009.
Shortly after Obama arrived in Saudi Arabia, Al Jazeera television aired a recording by Osama bin Laden in which he said the U.S. president had planted new seeds for "revenge and hatred" by pressuring Pakistan to crack down on militants in the Swat Valley, causing the mass exodus of refugees from the area.
Richard Holbrooke, the U.S. special envoy to Afghanistan and Pakistan, responded to the tape, saying that it is ludicrous to suggest that anyone but al-Qaida and the Taliban are responsible for the refugee crisis in Pakistan.
Pakistan says about 3 million people have been uprooted from their homes by a month-old campaign to drive militants out of the northwestern Swat valley.
Bin Laden warned Americans to be prepared for the consequences of the White House's actions. The authenticity of the tape could not be immediately verified.
Bin Laden, whose last message was released in mid-March, has been sparing in his criticism of President Obama in the past. In January, he said only that the U.S. president had received a "heavy inheritance" from his predecessor.
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