UPDATE 4-Saudi boosts oil output, ready to pump more

(Adds most of new supplies destined for U.S. buyers)

RIYADH, May 16 (Reuters) - The world's top oil exporter Saudi Arabia said on Friday it was ready to pump more oil if needed and has already made a modest output boost.

U.S. President George W. Bush met Saudi King Abdullah in Riyadh earlier on Friday to ask for more oil from OPEC to tame record oil prices.

The supplier of more than a tenth of the world's oil raised supplies by 300,000 barrels per day (bpd) a week ago to compensate for a fall in supplies from other producers, Saudi Oil Minister Ali al-Naimi said at a press conference.

"On May 10, we raised supplies to customers by increasing 300,000 barrels per day of oil (output)," Naimi said. "Therefore, production in June will be 9.450 million bpd ... In the future if the need appears, Saudi Arabia has no objection to producing more."

Naimi said most of the extra supplies would go to buyers in the United States, the world's largest energy consumer.

But Naimi told Bush and other U.S. officials in a presentation on Friday that an increase in oil output would not lead to a dramatic reduction in U.S. pump prices, a U.S. official said.

U.S. oil CLc1 was trading at $126 a barrel on Friday after hitting a record near $128.

The United States says more supply would help lower prices, while OPEC officials blame the high price on factors beyond their control, such as speculation and the weak dollar.