* U.S. crude inventories fall - EIA
* But exports surge, while net imports drop to record low
* U.S. crude output above 10 million bpd
* The U.S. shale revolution: http://tmsnrt.rs/2EtJgen (Re-leads with lower prices)
SINGAPORE, Feb 23 (Reuters) - Oil prices dipped on Friday as high U.S. crude exports outweighed lower crude inventories in the world's biggest consumer of the fuel.
U.S. West Texas Intermediate (WTI) crude futures were at $62.73 a barrel at 0449 GMT, down 4 cents from their last settlement.
Brent crude futures were down 6 cents at $66.33 a barrel.
Traders said crude was weighed down by demand entering seasonal lows as the northern hemisphere comes out of winter and by high U.S. exports.
U.S. crude exports jumped to just above 2 million barrels per day (bpd) last week, data from the Energy Information Administration (EIA) showed on Thursday, close to a record high of 2.1 million hit in October. That helped pull down net imports to the lowest level on record of below 5 million bpd.
U.S. crude oil production <C-OUT-T-EIA> was virtually unchanged last week at 10.27 million bpd, close to levels of top producer Russia and more than OPEC-kingpin Saudi Arabia pumps.
Prices were prevented from falling further by a decline in U.S. crude inventories, traders said.
U.S. crude oil stockpiles <C-STK-T-EIA> fell by 1.6 million barrels in the week to Feb. 16, to 420.48 million barrels, the EIA showed.
"Part of that (inventory fall) is the shape of the oil curve which makes it uneconomic to store product," said Greg McKenna, chief market strategist at futures brokerage AxiTrader.
The forward price curves for Brent and WTI are in a shape known as backwardation in which prices for immediate delivery are more expensive than those for later sale, making it uneconomical for traders to buy and store oil.
Globally, oil markets remain well supported due to demand-growth coinciding with production restraint led by the Organization of the Petroleum Exporting Countries (OPEC) and Russia.
(Reporting by Henning Gloystein; Editing by Richard Pullin and Kenneth Maxwell)