New York-traded cotton rose slightly on Tuesday, extending gains from the previous session, after speculation grew that global supplies of the fiber were not as high as recently estimated by the U.S. government, traders said.

The U.S. Department of Agriculture said last week global cotton inventories will reach a record 97.6 million 480-lb bales by the end of July. Cotton on ICE Futures U.S. fell after the estimate issued by the USDA on Friday, ending modestly lower, but at a 2-week low, and wiping out a rally in early trading.

The market rebounded 1.3 percent on Monday, after some traders reassessed the USDA report, which raised forecasts for cotton production for a fifth time since the agency's first outlook for the 2013/14 crop released in May.

On Tuesday, ICE Futures' most-active March cotton contract rose 0.5 cent to settle at 83.73 cents a lb.

"We were just going back and forth, trying to see if Friday's selloff was correct or yesterday's rally was," said Sharon Johnson, senior cotton analyst at KCG Futures in Roswell, Georgia.

The USDA's monthly report for January had forecast surprise increases in U.S. and Chinese cotton production, among others.

"There's a huge element of disbelief in the report," said Keith Brown, principal at cotton brokers Keith Brown and Co. in Moultrie, Georgia. "We all know China is cutting its cotton acreages and the U.S. production is as tight as it can be."

The USDA said China's share of global cotton supplies was expected to hit 58.3 million bales by July. It put U.S. ending stocks at around 3.0 million bales, similar to the previous crop year.

A Chinese industry group said last week that farmers in the country were expected to cut their cotton planting acreages by 9 percent this year.

Brown said U.S. ending stocks were expected to be closer to around 2.3 million bales. "We expect the USDA to scale back their estimates in the next monthly report," he said.