* U.S. daily crude output stays above 10 million barrels
* Libyan oilfield pumping 70,000 bpd shut - source
* U.S. crude inventories fall unexpectedly
* Saudi oil minister says oil market is rebalancing (Updates prices, adds Saudi quote)
LONDON, Feb 23 (Reuters) - Oil edged further above $66 a barrel on Friday supported by a dip in Libyan production and upbeat comments from Saudi Arabia that an OPEC-led effort to erode stockpiles through output curbs is working.
Crude rebounded from an early loss after the shutdown of the El Feel oilfield in Libya, which produces 70,000 bpd. Production in the OPEC member has been running at about 1 million bpd, although it remains volatile due to unrest.
Brent crude, the global benchmark, was up 10 cents at $66.49 at 1458 GMT. Prices had rallied in early 2018 and reached $71.28 on Jan. 25, the highest since December 2014. U.S. crude was up 8 cents to $62.85.
In the latest OPEC comment that a supply cut deal led by the Organization of the Petroleum Exporting Countries is working, Saudi Arabia's Energy Minister Khalid al-Falih said he expected inventories to keep declining this year.
"The oil markets, it's clear, are rebalancing," Falih, who is on a visit to India, said. "Many agencies have documented the decline in inventories and I think that'll continue in 2018."
Earlier, prices traded lower as rising U.S. oil production and exports weighed. Crude exports jumped to more than 2 million bpd, close to a record.
"The U.S. is pumping out a record amount of oil," said Naeem Aslam, chief market analyst at Think Markets UK Ltd. "The bull rally which we have seen for the black gold could fade away as the U.S. oil production undermines the OPEC production cut commitments," he said.
A stronger dollar also weighed on prices. A firmer dollar can make oil and other commodities denominated in the U.S. currency more expensive for other currency holders.
The latest decline for crude came despite the U.S. Energy Information Administration reporting crude stocks fell unexpectedly by 1.6 million barrels. Analysts said low import figures contributed to the decline.
U.S. production is expected to rise even more this year and top 11 million bpd in late 2018, a headwind for OPEC efforts to drain stockpiles.
In January 2017, OPEC and allies including Russia began to cut production by about 1.8 million bpd, almost 2 percent of global supply, to get rid of a glut that had built up since 2014 and that led to a price collapse.
OPEC wants to reduce inventories held by industrialized nations to their five-year average and is getting closer to that goal.
(Additional reporting by Henning Gloystein; Editing by Edmund Blair and David Evans)