* U.S. crude oil inventories rise slightly less than expected
* But U.S. crude stocks are still back above 5-year average
* U.S. crude output reaches another record at 10.37 mln bpd
By Henning Gloystein
SINGAPORE, March 8 (Reuters) - Oil prices steadied on Thursday after falling the previous day on the back of record U.S. crude production and rising inventories.
Brent crude futures were at $64.49 per barrel at 0100 GMT, up 15 cents, or 0.2 percent, from their previous close. That slight rise came after a more than 2 percent fall the previous day.
U.S. West Texas Intermediate (WTI) crude futures were at $61.29 a barrel, up 14 cents, or 0.2 percent. WTI also fell by more than 2 percent the previous session.
The slight recovery on Thursday came amid a U.S. crude inventory build that was not as big as expected during the current seasonal demand lull at the end of winter, when many oil refineries shut down for maintenance.
"Oil prices bounced back immediately after the release of the weekly oil inventories data from the Energy Information Administration ... (where) the headline figure was better than expected," said Fawad Razaqzada, market analyst at futures brokerage Forex.com.
The EIA reported late on Wednesday that U.S. crude inventories C-STK-EIA rose by 2.4 million barrels in the week to March 2, to 425.91 million barrels, less than the 2.7 million barrel increase analysts had forecast.
Despite this, oil markets remain under pressure from the seasonal trend of rising inventories, which in the United States have climbed back above the 5-year average of 420 million barrels.
Also looming over oil markets is soaring U.S. production, which last week marked another record, at 10.37 million barrels per day (bpd).
"Crude is ... under pressure from rising U.S. production which hit a new high last week, now firmly above Saudi Arabia's production level," said William O'Loughlin, investment analyst at Australia's Rivkin Securities.
At just below 11 million bpd, only Russia currently produces more crude oil than the United States, although the International Energy Agency (IEA) expects even this to change as the United States is set to surge past 11 million bpd by late 2018.
With U.S. output outpacing demand growth, analysts say the Organization of the Petroleum Exporting Countries (OPEC) and Russia, who together with some other producers have been withholding production in order to prop up prices, are under pressure to keep up the supply restraint, even at the cost of market share.
"OPEC may ... have to extend its production agreement with Russia and co in order to avoid triggering another 2014-style sell-off in oil prices," said Razaqzada.
Reporting by Henning Gloystein