June 6 (Reuters) -ICE cotton futures rose on Thursday for a third straight session, buoyed by support from firmer oil prices and strong demand from top consumer China.

* Cotton contracts for July CTc1 rose 0.94 cent, or 1.26%, at 75.38 cents per lb by 12:58 p.m. ET (1658 GMT).

* "Spot July is trying to keep the bid with shorts exiting in an orderly manner, the softs space higher, and a positive momentum in crude oil is also friendly for cotton," said Valentin Olah, risk management consultant at StoneX Group.

* China was an active buyer last week, with more than 50% of the commitments, and its presence added some short-term optimism, Olah said.

* The U.S. Department of Agriculture's USDA weekly report showed exports of 157,000 running bales (RB), down 9% from the previous week and 27% from the prior four-week average. EXP/COT

* The primary destination for exports was top consumer China, with 56,200 RB, the report added.

* Oil prices rose by more than $1 a barrel on Thursday as the European Central Bank cut interest rates for the first time in roughly five years and OPEC+ ministers reassured investors it could tweak its latest oil output agreement. O/R

* Higher oil prices make cotton-substitute polyester more expensive.

* Chicago Board of Trade corn Cv1 and soybean Sv1 futures rose as news of tighter rules on industry tax credits in Brazil made traders and producers hopeful that it could boost U.S. export business, traders said. GRA/

* In a weekly crop progress report on Monday, the USDA said 61% of the cotton crop was in good-to-excellent condition.

Reporting by Anushree Mukherjee in Bengaluru; Editing by Pooja Desai