President Bush on Tuesday gently nudged OPEC to raise production levels, saying he hopes the oil cartel will consider how high oil prices are straining the U.S. economy.

Bush said he is speaking with Saudi King Abdullah about oil prices, which recently surged past $100 a barrel.

"Oil prices are very high, which is tough on our economy," Bush said. "I would hope, as OPEC considers different production levels, that they understand that if ... one of their biggest consumers' economy suffers, it will mean less purchases, less oil and gas sold."

Bush spoke before he began a round-table with Saudi business men and women at the U.S. embassy. Secretary of State Condoleezza Rice, meanwhile, left the president's side and made a surprise visit to Baghdad on Tuesday for talks with Prime Minister Nouri al-Maliki. She was expected to push for more progress on political reconciliation.

Rice was already en route to Baghdad when her trip was announced as Bush kept to his schedule in the Saudi capital. Even before Bush left Washington, there was speculation that the president would be the one to stop in Iraq while he was in the Middle East.

The issue of high oil prices also has come up in earlier stops on Bush's eight-day trip to the region, largely in the context of his push for alternate fuels and sources of energy. White House counselor Ed Gillespie said Mideast leaders have talked to Bush about "the vast demand that's on the world market today for oil." He said that was "a legitimate and accurate point."

Saudi Arabia holds the world's largest oil reserves and surging fuel costs are hampering the economy in the United States where gasoline has topped $3 a gallon. High energy costs for fueling cars and heating homes are leaving people with less money to spend elsewhere, and prices for some other goods and services also have risen.

OPEC oil accounts for about 40 percent of the world's needs, and OPEC ministers often follow the lead of the Saudis when discussing whether to increase production to take the pressure off rising prices. The Saudis' views carry great weight because Saudi Arabia is responsible for almost a third of OPEC's total output.

Bush spoke before meeting with mostly young Saudi business owners, many of them educated in the United States. The group included two women. Bush appealed to one of Saudis' biggest gripes when he acknowledged the tight visa restrictions the United States imposed after the Sept. 11 terrorist attacks on Saudis trying to visit the U.S.

"The United States benefits when people come to my country," Bush said. "And one of my concerns was after September the 11th that our visa policy, particularly for Saudis, was tightened to the point where we missed opportunity to show young and old alike what our country is really about."

Later Tuesday, Bush was visiting al-Murabba Palace, the National History Museum and Al Janadriyah Farm, the Saudi Arabian king's country retreat where he maintains 150 Arabian stallions. That trip repays the visit of the king — when he was crown prince — to Bush's ranch in Crawford, Texas.

Cold, blustery winds blew in Saudi Arabia on Monday, but Bush received a warm embrace from the king, whose family wields almost absolute rule. Among ordinary Saudis and across much of the Mideast, Bush is unpopular, particularly because of the Iraq war and unflinching U.S. support for Israel. Bush and Abdullah were emphasizing their strong personal ties.

Abdullah presented Bush with what appeared to be a medallion of gold with white and green stones, suspended from a gold palm tree emblem with crossed swords.

"The least we can do in providing you hospitality is to provide you with the highest order of the Kingdom of Saudi Arabia, and that is the Order of the late King Abdul Aziz, founder of the Kingdom of Saudi Arabia," Abdullah said, speaking through a translator.

Bush, who dislikes late nights, stayed up well past his regular 9:30 p.m. bedtime for after-dinner talks with the king in the walled compound of his opulent palace. Its marble floors and walls contain sheets of gold, colored with precious stones and embedded jewels. U.S. officials said much of conversation over Monday's palace dinner was about chill temperatures that dropped into the 40s.

Earlier on Monday, Bush delivered a sophisticated weapons sale for Saudi Arabia, trying to bolster defenses against threats from U.S. adversary Iran and muster support in this oil-rich kingdom for a long-stalled Mideast peace agreement.

Coinciding with Bush's arrival, the administration officially notified Congress it will offer Saudi Arabia sophisticated Joint Direct Attack Munitions — or "smart bomb" — technology and related equipment. The deal envisions the transfer of 900 of the precision-guided bomb kits, worth $123 million, that would give Saudi forces highly accurate targeting abilities.

Some lawmakers fear the systems could be used against Israel but Congress appears unlikely to block the deal because of Saudi Arabia's cooperation in the war on terror and in deterring aggression from Iran.

The United States already has notified Congress of five other packages to Saudi Arabia, the United Arab Emirates and Kuwait, including Patriot missiles. The total amount of eventual sales as part of the Gulf Security Dialogue is estimated at $20 billion, a figure subject to actual purchases.

The sales are a key element in Bush's strategy to shore up defenses against Iran, which the president has deemed the world's top state sponsor of terrorism. Saudi Arabia and other Gulf states, with majority Sunni Muslim populations, harbor deep suspicions about Shiite Iran's rising power and want to make sure the U.S. remains committed to keeping Tehran's ambitions in check. At the same time, Arab allies are worried that the world economy would suffer heavily if the U.S. dispute with Iran turns into a military confrontation.

On Mideast peace, Saudi Arabia handed Bush a coup by taking part in the U.S.-sponsored Mideast peace conference in Annapolis, Md., in November. Bush was expected to encourage Saudi Arabia during his visit to use some of its vast wealth to help struggling Palestinians build the foundations of a future state. Bush also sees support from Arab neighbors as crucial to the Palestinian leadership being able to successfully negotiate with Israel over borders and other contentious issues.

Abdullah, for his part, was expected to urge Bush to keep up the pressure on Israel to halt settlements in Palestinian territories.