The upland cotton—the most commonly grown variety in the U.S. net export sales totaled 223,700 bales in the week ended Jan. 9, up 46% from the prior four-week average, the U.S. Department of Agriculture said. It was the largest sales number, minus any canceled orders, since the week ended Dec. 12. Demand for U.S. cotton is picking up, adding to concerns about the availability of supplies of the fiber.

Cotton traded on the ICE Futures U.S. exchange ended at 86.80 cents a pound Friday, putting the one-week gain at 5.1%, the biggest weekly increase since June.

Sales have been good. They've been pretty steady, said Michael Quinn, president of the Garner, N.C.-based Cotton Growers Cooperative, which sells cotton from 1,400 members

The U.S. exports more cotton than any other country in the world. Its biggest customers are in Asia, where mills spin the U.S. fiber into thread and yarn to make textiles.

But the most recent U.S. harvest, which ended last year, is also likely to be the smallest in four years: 13.2 million bales. That is the result of excessive rain in the Southeast U.S. last year and the decision by some growers to plant higher-priced crops, such as corn, instead.

However, the recent price gains could encourage growers to plant more cotton this spring.

This is making cotton more competitive, said Sterling Smith, a futures specialist at Citigroup. C -0.63% He added, however, that they are still at the guessing stage.

The first estimates for cotton planting won't be released until February. Until then, the market will be keeping an eye on how well U.S. cotton is selling.

The next export-sales report, due Friday, could also be a "game changer," said Michael Sweeney, a senior cotton broker at Marex Spectron in New York. If export sales fell last week, prices could follow suit.