* Southeast rains, Texas conditions drive limited buying

* Fiber reverses losses to edge up for second session

* Weekly U.S. export sales, shipments down -USDA data

NEW YORK, July 25 (Reuters) - ICE cotton eked out a gain for a second straight session on Thursday, withstanding pressure from falling grains and financial markets as worry over upcoming supplies in the United States, the world's top exporter, drove limited buying.

The most-active December cotton contract on ICE Futures U.S. closed up 0.25 cent, or 0.3 percent, at 85.99 cents a lb.

Dealers said merchant short-covering on producer selling and new speculator buying has been behind the limited gains.

Fiber was steady, underpinned by expectations of a delayed crop after dry weather in Texas earlier in the season, and by ongoing rains in the southeastern United States.

Some of the crop is "in big-time jeopardy because of adverse growing conditions," said Keith Brown, president of commodity firm Keith Brown and Co in Moultrie, Georgia.

The buying came as favorable crop weather drove steep losses in the grains markets and as global equity markets eased on renewed concerns that economic growth is slowing in China.

Exchange stocks continued their fall to the lowest level in five months, ICE data showed, also lending support to prices.

Concern that nearby supplies will be tight if fiber demand picks up at the start of the 2013/14 crop year that begins on Aug. 1 has left December cotton at a premium to the March 2014 contract of 1.73 cents per lb, up from 1.56 cents previously.

The backwardated market is seen as unusual for a market that is forecast to hold record inventories.

Gains remained capped by expectations of climbing global output and worries that high prices will crimp demand.

Heavy monsoon rains forecast for next week will improve the cotton crop in India, the world's second largest producer. Earlier this month, the U.S. Department of Agriculture (USDA) revised higher its forecast for global production due to favorable weather in India.

U.S. export sales and shipments were down in the week ended July 18 from the previous week, USDA data showed.

The week's decline came despite an increase in sales to China, eagerly eyed by global traders as recent economic data has prompted worry over a slowdown in the world's top consumer of many raw materials, including cotton. (Reporting by Chris Prentice; Editing by Peter Galloway)