UPDATE 3-Oil prices stable as lower crude stocks counter soaring US output

* U.S. crude production rises 25,000 bpd to 9.71 mln bpd

* U.S. crude stocks down by 5.6 mln barrels at 448.1 mln

* Gasoline stocks gain 6.8 mln barrels to 220.9 mln (Recasts, updates prices)

SINGAPORE, Dec 7 (Reuters) - Oil prices were stable on Thursday as a fall in U.S. crude inventories was countered by soaring output and a rise in fuel stocks.

U.S. West Texas Intermediate (WTI) crude futures were at $55.95 a barrel at 0658 GMT, virtually unchanged from their last settlement.

Brent crude futures, the international benchmark for oil prices, were at $61.29 a barrel, up 7 cents.

U.S. crude oil inventories fell by 5.6 million barrels in the week to Dec. 1, to 448.1 million barrels <C-STK-T-EIA>, putting stocks below seasonal levels in 2015 and 2016.

Despite this, prices were prevented from rising further.

"Traders were more concerned about the steep rise in gasoline inventories," said Stephen Innes, head of trading for Asia-Pacific at futures brokerage OANDA in Singapore.

Gasoline stocks rose 6.8 million barrels, to 220.9 million barrels, according to the report from the U.S. Energy Information Administration (EIA), much more than analyst expectations in a Reuters poll for a gain of 1.7 million barrels.

"This suggests that refiners may not need to process as much crude in the future," ANZ said in a note on Thursday.

"The EIA report also showed that U.S. production increased again," the bank said.

U.S. crude production <C-OUT-T-EIA> climbed by 25,000 barrels per day (bpd) to 9.71 million bpd, the highest since monthly figures showing the United States produced more than 10 million bpd in the early 1970s.

Soaring U.S. output threatens to undermine efforts led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia to bring production and demand into balance following years of oversupply.

Sukrit Vijayakar, managing director of energy consultancy Trifecta warned there were "darker shadows over the pace of rebalancing, if at all any is taking place."

(Reporting by Henning Gloystein; Editing by Joseph Radford and Tom Hogue)