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* Cotton sinks for third session this week
* Fiber set to post weekly following 5-week price rally
* U.S. export levels seen falling in response to higher prices
By Chris Prentice
NEW YORK, Feb 7 (Reuters) - U.S. cotton futures fell for a third time this week to a one-week low on Thursday, as a second week of lower U.S. weekly export sales data heightened concerns that high prices have begun to deter demand from China, the world's largest consumer.
The most-active March cotton contract on ICE Futures U.S. settled down 0.32 cent, or 0.4 percent, at 81.40 cents per pound, the lowest price since Jan. 28.
The loss on Thursday, cotton's third down day during the week, put the fiber on track for its first weekly loss in six weeks. Prices have fallen about 2 percent since Friday's close.
The flagging momentum comes after cotton reached a seven-month high of 84 cents on Jan. 24 and rallied 10.5 percent in January, outperforming the rest of the Thomson Reuters-Jefferies CRB index.
"This price level is high enough to start limiting demand," said John Flanagan, an analyst at Flanagan Trading Corp. in North Carolina.
That constricted demand was apparent in the USDA's weekly export figures, released Thursday, which showed that total exports had fallen for a second week in a row.
Sales totaled 93,600 running bales of upland cotton in the week ended Jan. 31, down 58 percent from the four-week average.
China was on the sidelines, buying just 1,100 bales, compared to average levels of about 122,000 bales bought each of the previous eight weeks reported.
In last week's data, buyers in China had canceled bales for the first time since mid-July.
Cotton has seen a more long-term erosion in demand as consumers turned to lower-price synthetic alternatives to the natural fiber.
Trading volumes were heavy on Thursday, reaching more than 41,000 contracts and well above a 250-day average of under 19,000 lots, according to preliminary Thomson Reuters data.
Open interest climbed for eight straight sessions and reached a two-year high on Wednesday, ICE data showed.
The rise in open interest has come as speculators have boosted their bullish stance in cotton to a two-year high, U.S. Commodity Futures Trading Commission data shows.
The heavy volumes were seen as likely to continue into Friday, with the triple whammy of the U.S. Department of Agriculture's monthly crop report, the expiration of March options, and the start of the index fund rolls.
"The thing to watch there is what the USDA does with world consumption," Flanagan said.
Last month, prices rose after the USDA cut its forecast for both U.S. cotton production and U.S. season-ending stock levels for the 2012/13 season. (Reporting By Chris Prentice and M.D. Golan)