July 7 (Reuters) -ICE cotton futures firmed on Friday, aided by a softer dollar, although a weaker export sales report and falls across wider financial and commodity markets limited further gains.

* The most-active December cotton contract CTz3 gained 1 cent, or 1.3%, at 80.9 cents per lb by 12:11 a.m. EDT (16:11 GMT). It traded in a range of 79.6 and 81 cents a lb. Prices were up 0.6% for the week thus far.

* "There is pressure on dollar, which is certainly lending a little bit of support to cotton prices," said Bailey Thomen, risk management consultant at StoneX Group.

* The dollar index .DXY was down 0.9%, making the natural fiber more appealing to other currency holders. USD/

*The U.S. Department of Agriculture's (USDA) weekly export sales report showed net sales of 109,200 running bales (RB) for 2022/2023, down 13% from the previous week and 42% from the prior 4-week average.

* "Exports of 4,200 RB were down 72% from the previous week and 46% from the prior 4-week average," the USDA report added.

* Capping gains for cotton, Wall Street's main indexes and oil prices fell on Friday. .N O/R

* Lower oil prices make polyester, a cotton substitute, less expensive.

* In the grains market, Chicago corn futures fell on expectations of some welcome rains in the U.S. grain belt. GRA/

* The USDA's weekly crop progress report on Tuesday showed 48% of U.S. cotton acreage was rated in good-to-excellent condition, up marginally from 44% a year ago.

* "Portions of west Texas and the Panhandle area have received rainfall over the past couple of weeks but the amount is still below normal in some of those areas," Don Shurley, professor emeritus of cotton economics at University of Georgia wrote in a note dated Thursday.

Reporting by Ananya Bajpai in Bengaluru; editing by Barbara Lewis