Cotton contracts for December rose 0.01 cent, or 0.02%, to 62.29 cents per lb as of 2:01 p.m. EDT (1801 GMT). It traded within a range of 61.88 and 62.78 cents a lb.
The December contract gained about 6.3% last week, its best since the week ended June 1, 2018.
"There seems to be support for cotton after the recent rally, but there is not much incentive to push prices higher," said Barry Bean, a cotton buyer based in Gideon, Missouri.
"Even if Washington and China were able to resolve their differences by October, we are looking at a long road to recovery. We have a large US crop and world crop. Between now and the end of the year, there is support at around 55 cents, but there is also a strong resistance around 63 cents as we are seeing today."
Last week, World Agriculture Supply and Demand Estimates (WASDE) report forecast world ending stocks for 2019/20 to be 1.3 million bales higher than last month's forecast.
Prices have fallen over 15% so far this year on the backdrop of the protracted trade war between the United States and China, one the leading consumers of the natural fibre.
Total futures market volume fell by 11,794 to 25,885 lots. Data showed total open interest fell 1,292 to 233,028 contracts in the previous session.