* U.S. crude stocks down by 5.6 mln barrels at 448.1 mln
* But U.S. crude production rises 25,000 bpd to 9.71 mln bpd
* Gasoline stocks up 6.8 mln barrels, to 220.9 mln (Adds comment, updates prices)
SINGAPORE, Dec 7 (Reuters) - Oil prices inched up on Thursday on a decrease in U.S. crude inventories, but rising gasoline stocks and crude production weighed on the market.
U.S. West Texas Intermediate (WTI) crude futures were at $56.09 a barrel at 0101 GMT, up 13 cents, or 0.23 percent from their last settlement.
Brent crude futures, the international benchmark for oil prices, were at $61.32 a barrel, up 10 cents, or 0.16 percent.
Traders said the higher prices came as 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.
The slightly higher prices came after a much bigger sell-off in late U.S. trading.
"WTI prices cratered (on Wednesday) despite a drop in weekly crude inventories. Indeed, 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, 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 on Thursday.
"The EIA report also showed that U.S. production increased again," the bank added.
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.
(Reporting by Henning Gloystein; Editing by Joseph Radford)