* U.S. crude stocks down for 4th straight week
* But U.S. production rises close to 10 mln bpd (Adds OCBC comment, U.S. output data; updates prices)
SINGAPORE, Dec 14 (Reuters) - Oil markets rose on Thursday, lifted by a fourth straight weekly fall in U.S. crude inventories, though climbing output capped prices well below the 2015 highs reached earlier this week.
U.S. West Texas Intermediate (WTI) crude futures were at $56.77 a barrel at 00344 GMT, up 17 cents, or 0.3 percent, from their last settlement.
Brent crude futures, the international benchmark for oil prices, were at $62.81 a barrel, up 37 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 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.
Another cap on prices has been soaring U.S. production <C-OUT-T-EIA>, which has risen by 16 percent since mid-2016 to 9.78 million barrels per day, the highest since the early 1970s and close to levels from top producers Russia and Saudi Arabia.
Singapore's OCBC bank said on Thursday in its 2018 commodities outlook that a "further rise in prices could well be met by stronger U.S. production as shale oil players turn taps on," suggesting that oil prices may not rise too far in 2018.
"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 and Joseph Radford)