The Saudis are sponsors of the only comprehensive peace plan for relations between the Arab world and Israel, although peace negotiations are at a standstill.
Egypt is intimately involved with the Palestinian problem, acting as an intermediary between Israel and Hamas in the Gaza Strip.
In Riyadh, Mr Obama's motorcade took him to the ranch of King Abdullah, proceeding up a long drive lined with Saudi horse guards before arriving at a palatial meeting room.
The king and president sat side-by-side chatting and smiling ahead of private talks.
King Abdullah presented Mr Obama with a large gold medallion which he placed around the president's neck.
Mr Obama said that in previous conversations with the king he had been struck by his "wisdom and graciousness".
"I thought it was very important to come to the place where Islam began and to seek his majesty's counsel and to discuss with him many of the issues that we confront here in the Middle East," he said.
"I am confident that working together, the United States and Saudi Arabia can make progress on a whole host of issues of mutual interest."
On the ground as Obama arrives in Riyadh
Mr Obama is not expected to make any major statements in Riyadh, but on Thursday, he is to deliver
a speech at Cairo University
which our correspondent says could be one of the most important of the Obama presidency.
Mr Obama's tour has come amid a flurry of messages purportedly from al-Qaeda militant leaders, including a rare recording from the group's figurehead, Osama Bin Laden.
According to a tape transmitted by Arabic TV station al-Jazeera as Air Force One arrived in Riyadh, Bin Laden accuses the US president and his predecessor, George W Bush, of planting seeds to increase hatred of America.
"The number of these seeds is equal to the number of displaced people from Swat valley," it said.
US pressure on Pakistan had led to a campaign of "killing, fighting, bombing and destruction" that prompted the exodus of a million Muslims from the Swat valley, the recording added.
Earlier, a deputy leader of al-Qaeda
urged Muslims to ignore the new tone from Washington, because Mr Obama's "bloody messages" - in Iraq and Afghanistan - would not be concealed by "polished words".
Al-Qaeda in Saudi Arabia issued an internet statement vowing to target President Obama's convoy in Riyadh.
The tour itinerary does not include Israel, but shortly before departing for Saudi Arabia, Mr Obama had a meeting with Israel's defence minister, Ehud Barak, in Washington.
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