May 22 (Reuters) -ICE cotton futures fell on Monday, pressured by a stronger dollar, with lingering concerns about the U.S. debt ceiling also weighting on sentiment.

* The most active first-month July cotton contract CTc1 fell 1.70 cent, or nearly 2% at 85.02 cents per lb, at 12:03 p.m. ET, trading within a range of 84.61 and 87.25 cents a lb.

* "The cotton market is focusing on the debt ceiling talks in Washington more than anything," said Keith Brown, principal at cotton broker Keith Brown and Co in Georgia, adding a deal would be ultimately positive for commodities and stocks overall.

* Some scattered rain in the key growing region of West Texas could also be weighing on the market, Brown added.

* Cotton futures saw their best week since late November in the week of May 19.

* "The bulk of the surge is simply due to basic fundamental supply and demand – a tight projected balance sheet that could get tighter, mostly based on supply concerns," Louis Rose of Tennessee-based Rose Commodity Group wrote in a note.

* A higher dollar also made greenback-priced cotton less attractive, especially for overseas buyers. USD/

* In the wider grains market, Chicago wheat futures fell below $6 a bushel for the first time in more than two years as expectations of ample global supplies weighed on prices after a wartime deal to ship Ukrainian grains was extended last week. GRA/

Reporting by Seher Dareen in Bengaluru; Editing by Maju Samuel