RIYADH, Saudi Arabia (CNN) -- Saudi Arabia Friday rebuffed President Bush's request to immediately pump more oil to lower record prices, saying it does not see enough demand to increase production.

The Saudis said they would increase production if customers demanded it, Steven Hadley, Bush's national security adviser, said.

Ali al-Naimi, the Saudi oil minister, on Friday said the country had increased its production by 300,000 barrels a day on May 10 in response to customer requests.

Al-Naimi said the increased production would bring Saudi Arabia's daily production to 9.45 million barrels per day by June.

Bush is spending much of the day in closed-door meetings with King Abdullah, the Saudi ruler.

Friday's visit was Bush's second trip to the kingdom this year, coming as oil prices reached a new record high Friday of more than $127 a barrel. When he traveled to Riyadh in January, his request for the Saudis to pump more oil was also rejected.

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Oil prices were just below $100 a barrel in January, and Americans were paying an average of $3.06 for a gallon of gasoline. They were paying $3.78 on Friday, following more than week of record highs every day.

"Clearly, the price of gas is too high for Americans, and it's causing a hardship for many families of low income. But it also is not allowing our economy to grow as strong as it could," spokeswoman Dana Perino said en route to Saudi Arabia.

"One of the best ways to have lower prices is if there was a better calibration between the laws of supply and demand. We have little -- not enough supply, and too high demand. Trying to get more supply out there is good for everyone," she said.

But Saudi Arabia -- and many economists -- say the high prices are a result of market speculation, the weak dollar, and demand from the developing world rather than a shortage of supply.

"We will raise production when the market justifies it. This is our policy," al-Naimi said during Bush's first visit in January. "Our interest is to hopefully keep supply matching demand with minimum volatility in the international oil market," he added.

Saudi Arabia maintains spare production capacity of about 2 million barrels per day use when there is "an unexpected need," al-Naimi said in January.

Bush will also discuss oil industry security and peaceful nuclear cooperation with the Saudis. The trip, part of a Middle East tour that began in Israel and will continue to Egypt, marks the 75th anniversary of diplomatic relations between Washington and Riyadh.

CNN's Ed Henry contributed to this report.

All About Saudi Arabia • Oil Production and Refining • George W. Bush