(Adds byline; comments by Japan's Fujii, paragraphs 11-12;details)

By Glenn Somerville

TOKYO, Nov 10 (Reuters) - U.S. Treasury Secretary Timothy Geithner on Tuesday told his Japanese counterpart that a commitment by Tokyo to rely less on exports and more on domestic consumption to power growth will benefit the global economy.

According to a senior U.S. Treasury official who spoke to reporters from Singapore, Geithner told Japanese Finance Minister Hirohisa Fujii at a dinner meeting that he welcomed a commitment by Japan to "shift its economy away from exports toward demand-led growth."

Geithner, making his first trip to Japan since becoming U.S. U.S. Treasury chief last January, was continuing a drive to get Asian countries, including China, to do more to spur their own economies through encouraging consumption in a bid to get global trade flows into better balance.

He arrived in Tokyo late on Tuesday afternoon and will spend much of Wednesday meeting top Japanese officials, including Prime Minister Yukio Hatoyama, before flying on to Singapore for sessions on Thursday of the 21-nation Asia-Pacific Economic Cooperation forum, or APEC.

In response to questions, the U.S. official, who spoke on condition of anonymity, said China also had a role to play by exporting less while countries like the United States begin to save more and suggested a more flexible currency would help.

"I think first I'll say we welcome the commitment to move to a more flexible exchange rate over time," the U.S. official said. "Flexible prices, flexible exchange rates are an important part of the process for rebalancing and are important for China."

The Obama administration has twice turned down a chance to name China a currency manipulator in reports to Congress but leaves no doubt it is in favor flexible currencies whose values fluctuate in company with the strength of their economies.