RIYADH, Saudi Arabia | Regular gasoline goes for less than 50 cents a gallon in Riyadh, the capital of the world's largest producer of oil, pumping out 9 million barrels a day.

But, after a visit with the Saudi monarch in Riyadh, President Bush has found little hope of bringing any significant relief back home, where Americans are paying close to $4 a gallon.

The Saudis have agreed to a relatively modest boost in oil production, announced in the midst of meetings Friday with King Abdullah over tea, lunch and dinner and an overnight stay for Bush at the palatial horse farm where the Saudi ruler keeps 150 Arabian stallions in air-conditioned stalls.

But, for the second time in five months, the Saudis have rebuffed the Bush administration's request for significantly stepped-up oil production to ease rising oil prices. The Saudi oil minister said the Saudis already had marginally boosted production by about 300,000 barrels a day, as of May 10, to meet world demand, as they see it. This will boost output to 9.45 million barrels a day in June.

The Saudis have made clear they see no great world demand for increased production, Stephen Hadley, the president's national security adviser, said after private meetings between Bush and Abdullah at the king's ranch. And they are not bowing for one customer, albeit the world's biggest consumer.

'What they're saying to us is ... Saudi Arabia at the present time does not have customers that are making requests for oil that they are not able to satisfy,' Hadley said. And despite the production boost announced 'in order to meet the demand of their customers, in their judgment ... even increased production under this policy would not result in [a] dramatic ... reduction of gas prices in the United States.'

The talks were conducted in private, but both sides spoke about them afterward. Prince Saud al-Faisal, the Saudi foreign minister, was asked how forcefully Bush had made the case for boosting production.

'The discussion was carried out in a friendly fashion,' al-Faisal told reporters.

'I don't know what you mean by forcefully — he didn't punch any table or shout at anybody. ... The president showed great concern for the impact on the American economy ... and we, of course, sympathized with that completely. But on our part, we are doing everything we can to help the international economy by producing as much as is needed.'

During the talks, the discrepancy between gas prices in the land of plenty and in the land of the 'oil-addicted,' as Bush has called the U.S., could hardly be more dramatic: Gas fetches about 46 cents a gallon on the furnace-hot streets of Riyadh, and a gallon of regular in the U.S. has reached an average of $3.73.

The Bush administration repeatedly has tried to convince the Saudis that the impact of soaring gas prices on the American economy is bad, in the long run, for the profits of the oil producers. They 'need to take into account the economic health of their customers who pay these prices,' Hadley had said before this visit.

But the president's appeals for stepped-up production — an appeal that Bush personally made to the king in January, when the price of oil still hovered below $100 a barrel — conflicts with a firm Saudi practice of matching oil output with demand and maintaining stability in the world's oil market, while heeding to production quotas set by the Organization of Petroleum Exporting Countries.

While stepped-up production could alleviate pressure on rising prices, analysts say, the Saudis, who produce one-tenth of the world's oil, have no incentive to assist the United States alone.

'The reality is the market isn't being driven by us,' said Anthony Cordesman, a senior fellow at the Center for Strategic and International Studies.

'It's being driven by China, by India, by rising Asian demand, which guarantees a market into the long term.'

Oil is the mainstay of the Saudi economy. It was first discovered here in the 1930s, but large-scale production started after World War II. Now, more than $200 billion in oil products a year is exported, 90 percent of the nation's economy.

The opulence of the oil-rich Saudi royalty is seen at the lavish horse farm of the king, Al Jamadriyah Ranch, sitting on 'thousands of hectares' outside Riyadh.

The home, constructed as a tent with a permanent roof and poles made of ebony, ivory and precious stones, is divided into two chambers — one a throne room with space for 200, the other a dining room with capacity for 300. Like many Americans, the king has a television at his dinner table, albeit an 80-inch flat screen.

The Bush administration is honoring the 75th year of formal relations with the Saudis — cemented with an agreement Friday to cooperate on security, nuclear energy and nonproliferation of nuclear weaponry — but the Bush family and the House of Saud also go way back.