Oct 13 (Reuters) - ICE cotton futures edged up for a third straight session on Tuesday as increasing fears regarding sizeable damage to the crop from Hurricane Delta countered pressure from a rising U.S. dollar.

* Cotton contract for December  rose 0.24 cent, or 0.4%, to 68.61 cents per lb, at 1:28 pm EDT (1728 GMT). It traded within a range of 68.26 and 69.25 cents a lb.

* The December contract was still hovering below its highest in nearly eight months, hit in the previous session.

* Due to "last week's hurricane, that came through the delta region, there was several inches of rainfall and that is detrimental to the crop at this stage," said Bailey Thomen, cotton risk management associate with StoneX Group.

* "We are also seeing some carryover from grains market," Thomen said adding, the recovery in the dollar was slightly weighing on the natural fiber and would have a bigger impact leading to a downward price correction if greenback continues to rise.

* Chicago soybean and wheat futures rose on Tuesday, while CBOT corn gained on fresh export sales to Mexico.

* The dollar was up 0.5% against key rivals as investors turned cautious after a Johnson & Johnson Covid-19 study was paused while a gauge of inflation rose for a fourth straight month.

* Market participants are awaiting the U.S. Department of Agriculture's weekly crop progress estimates, due later in the day.

* Total futures market volume fell by 17,241 to 17,306 lots. Data showed total open interest gained 1,949 to 232,904 contracts in the previous session. (Reporting by K. Sathya Narayanan in Bengaluru; Editing by Richard Chang)