* U.S. crude stocks down fourth straight week
* Ongoing Forties pipeline outages also supports crude
* But U.S. production rises to nearly 10 mln bpd (Adds Forties comment, 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 $56.69 a barrel at 0545 GMT, up 9 cents, or 0.2 percent, from their last settlement.
Brent crude futures, the international benchmark for oil prices, were at $62.79 a barrel, up 35 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 decline, to 442.99 million barrels, lowest since October 2015.
Despite the price gain, Brent was well below $65.83 a barrel, the June 2015 high touched earlier this week. It hit that level after the Forties pipeline - which carries significant amounts of the North Sea crude used to underpin Brent crude futures - was shut down due to cracks.
The International Energy Agency has said it saw no immediate need to act, for instance with the release of strategic stockpiles, as the market remains well supplied.
"The next four weeks or so should be interesting. If the market is able to survive without the Forties supply, its returning on stream could trigger a major sell-off," said Sukrit Vijayakar, director of energy consultancy Trifecta.
Another cap on prices has been soaring U.S. oil 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 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 Joseph Radford and Tom Hogue)