April 4 (Reuters) -ICE cotton futures fell for a third consecutive session on Thursday on subdued demand outlook for the natural fiber.

* Cotton contract for May CTc1 fell 1.55 cent, or 1.74%, at 87.43 cents per lb by 13:15 p.m. ET (1715 GMT), its lowest level since Feb. 7.

* "Cotton has no friends again today," said Jim Nunn, owner of Tennessee-based cotton brokerage Nunn Cotton, adding that lower demand and the inversion between higher old crop prices versus the lower new crop prices is pressurising the market.

* The U.S. Department of Agriculture's (USDA) weekly export sales report showed net sales of 84,900 running bales for 2023/2024, down 14% from the previous week, but up 4% from the prior 4-week average.EXP/COT

* The report also showed exports of 367,600 running bales, up 2% from the previous week and 7% from the prior 4-week average.

* "I would suspect that the market is going to try and make a correction and start to rally back on technical buying," said Jon Marcus, president of Lakefront Futures and Options brokerage, in Chicago.

* Certified cotton stocks, which can be delivered against the contract, were at 92,654 bales compared with 67,576 bales on April 1, according to ICE data.

* Speculators cut net long position by 5,301 contracts to 58,373 contracts in ICE U.S. cotton futures in the week of March 26.CFTC/

* Meanwhile, Chicago corn, wheat and soybeans ticked higher, consolidating after a day-earlier rebound as market participants awaited further pointers on U.S. spring planting and turned their attention to U.S. jobs data. GRA/

Reporting by Anushree Mukherjee in Bengaluru; Editing by Ravi Prakash Kumar