Oct 17 (Reuters) - ICE cotton futures edged higher on Tuesday, supported by short-covering and mill fixations, but harvest pressure in the United States capped gains.

Cotton contracts for December settled up 0.24 cent, or 0.36 percent, at 67.77 cents per lb. They traded within a range of 67.45 cents, the lowest since Oct. 3, and 68.6 cents a lb.

Investors covering their shorts earlier in the day pushed the market higher, but harvest pressure came back later in the day and prices settled only marginally higher, according Rogers Varner, president of Varner Brokerage in Cleveland, Mississippi.

On Monday, the U.S. Department of Agriculture's (USDA) weekly crop progress report showed 31 percent of cotton crop was harvested in the United States by the week ended Oct. 15. It rated 58 percent of the U.S. cotton crop in good to excellent condition, down from 60 percent a week ago but up from 47 percent year ago, the report said.

"Cotton found some upside movement ... fundamentally on continued mill fixation of on-call sales," Louis Rose, co-founder and director of research and analytics at Rose Commodity.

Total futures market volume fell by 1,922 to 21,124 lots. Data showed total open interest fell 709 to 229,193 contracts in the previous session. Certificated cotton stocks deliverable as of Oct. 16 totaled 5,705 480-lb bales, down from 6,584 in the previous session.

(Reporting by Nithin Prasad in Bengaluru; Editing by Meredith Mazzilli)