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Oil rises on lower U.S. crude stocks, but growing output caps gains

* U.S. crude stocks down for 4th straight week

* But U.S. production rises close to 10 mln bpd

SINGAPORE, Dec 14 (Reuters) - Oil prices rose on Thursday, lifted by a fourth straight weekly fall in U.S. crude inventories, though rising output capped prices well below the 2015 highs reached earlier this week.

U.S. West Texas Intermediate (WTI) crude futures were at $56.81 a barrel at 0123 GMT, up 21 cents, or 0.4 percent, from their last settlement.

Brent crude futures, the international benchmark for oil prices, were at $62.84 a barrel, up 40 cents or 0.6 percent from their last close.

U.S. crude oil stockpiles fell by 5.1 million barrels in the week to Dec. 8, the fourth consecutive week of declines, to 442.99 million barrels the lowest since October 2015.

Despite the rise, Brent was well below the $65.83 a barrel June 2015 high reached earlier this week. It hit that level after the Forties pipeline in the North Sea, which carries significant amounts of crude used to underpin the Brent crude futures, was shut down due to cracks.

The International Energy Agency said it saw no immediate need to act, for instance with the release of strategic stockpiles, as the market remains well supplied.

"A decline in the open interest on the Brent crude oil future...is pointing towards some year-end profit-taking after the latest leg-up in prices," said Ole Hansen, head of commodity strategy at Denmark's Saxo Bank.

"A lot of, perhaps all, the current news about tightness in the oil market is already priced in," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.

(Reporting by Henning Gloystein; Editing by Kenneth Maxwell)