March 3 (Reuters) -ICE cotton futures gained on Friday, helped by a softer U.S. dollar and firm equities market, but the natural fiber was still on track for a weekly fall due to a weak export sales report.

* The cotton contract for May CTc2 rose 0.36 cent, or about 0.4%, to 84.07 cents per lb at 11:36 a.m. EST (1636 GMT).

* The contract is down 0.9% so far this week.

* The U.S. dollar index .DXY is headed for its first weekly loss in five, making cotton less expensive for other currency holders. USD/

* U.S. stocks rose on Friday as Treasury yields took a breather from a week-long rally that was sparked by Federal Reserve rate-hike worries. .N

* The cotton market is still digesting Thursday's disappointing export sales report, said Valentin Olah, cotton risk management consultant at StoneX Group.

* Cotton contract for May looks a little bit vulnerable as nearby technicals took damage from yesterday's selloff. However, there is still some buying interest around the high 83 cents region and that is positive, Olah said.

* "It has again become sensible to the U.S. dollar which has been modestly lower to lend support."

* Cotton prices fell more than 2% on Thursday after the U.S. Department of Agriculture's weekly export sales report showed net sales of 170,600 running bales of cotton for 2022/2023, down 60% from the previous week and 37% from the prior four-week average. EXP/COT

* Elsewhere, Chicago grain futures edged higher but were poised for weekly losses, despite some support from concerns about soybean supply from top producer Argentina amid dry weather conditions and worries about Ukrainian corn and wheat supplies. GRA/

* "Domestically, the mid-south and much of southeastern states continue to be pummeled by rainfall and severe weather, which are keeping farmers out of fields for pre-planting work," Louis Rose of Tennessee-based Rose Commodity Group wrote in a note.

Reporting by Harshit Verma in Bengaluru; Editing by Shilpi Majumdar