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UPDATE 7-Oil steady after surprising increase in U.S. crude exports

* Brent/WTI spread narrows on record U.S. exports

* Analysts say oil markets have largely rebalanced

* U.S. rig count suggests further rise in shale output (New throughout, updates prices and market activity, adds U.S. inventory figures, U.S.-Brent spread, new byline, dateline, previous LONDON)

NEW YORK, Oct 4 (Reuters) - Oil prices were little changed on Wednesday, though U.S. futures caught a bit of a bid against the Brent benchmark after a surprising jump in U.S. exports to a record 2 million barrels a day.

U.S. crude stocks fell sharply last week, but crude exports rose to 1.98 million barrels a day, the Energy Information Administration said.

U.S. exports became more attractive to buyers because the price of U.S. West Texas Intermediate crude was at a steep discount to Brent, which still has a $5 premium to WTI. Rising U.S. production has held down WTI prices, while Brent's price is heavily influenced by policy directions from OPEC.

November U.S. crude was up 2 cents to $50.47 as of 11:16 a.m. EDT (1516 GMT); Brent was down 11 cents to $55.87 a barrel.

The spread between the December contracts narrowed to $5.16 from $5.31 before the data.

U.S. crude inventories fell 6 million barrels in the week to Sept. 29, a much bigger decline than the decrease of 756,000 barrels analysts had expected. Gulf Coast refineries have been using more crude as they resumed operations after weeks of shutdowns following Hurricane Harvey.

Strategists viewed Brent as pricey after a third-quarter rally lifted it to mid-2015 highs by late September. A resumption in output at Libya's Sharara oilfield fed the concerns.

"Fundamentals may not yet be strong enough to support a continued rally, especially in growth-dependent commodities such as oil," Ole Hansen, head of commodity strategy at Denmark's Saxo Bank, said in a quarterly outlook to investors.

The Sharara oilfield restarted on Wednesday. It had been producing more than 230,000 barrels per day (bpd) before armed brigades closed it on Sunday.

Observers said a market rebalancing was well underway as a result of strong consumption and output cuts led by the Organization of the Petroleum Exporting Countries.

On Wednesday OPEC Secretary-General Mohammad Barkindo said he was confident his organization could restore sustainable stability to markets. Russian President Vladimir Putin said he did not exclude an extension of output cuts until the end of 2018. Russia is part of the supply agreement.

Rising oil production in the United States, which is not involved in the deal, has limited price gains. U.S. output <C-OUT-T-EIA> hit 9.56 million bpd at the end of September, highest since July 2015, and drillers added six oil rigs in the week to Sept. 29, according to energy services firm Baker Hughes. <RIG-OL-USA-BHI>

(Additional reporting by Libby George and Ron Bousso in London; Henning Gloystein in Singapore and Scott DiSavino in New York; Editing by Dale Hudson and David Gregorio)