(New throughout, updates prices, market activity and comments tgo include U.S. trading; new byline, changes dateline, previous SINGAPORE/PARIS)

CHICAGO, June 7 (Reuters) -

U.S. wheat futures fell on Wednesday, with the most-active Chicago Board of Trade soft red winter wheat contract snapping a five-session rally that had stoked worries about the demand outlook for U.S. offerings on the export market, traders said.

Recent price gains had pushed futures to their highest in nearly three weeks.

"Does this market have enough to justify going higher when Russia continues to dump wheat on the market?" StoneX chief commodities economist Arlan Suderman said. "Russia still sets the world wheat market price."

Corn futures were steady to lower, with contracts that track the recently seeded crop posting the biggest declines on forecasts for some rains in key growing areas of the Midwest this weekend. The weakness in wheat added pressure to the corn market.

Soybeans were higher, with traders

staking out positions

ahead of the U.S. Agriculture Department's closely watched World Agricultural Supply and Demand Estimates report on Friday.

At 11:42 a.m. CDT

(1642 GMT)

, the benchmark Chicago Board of Trade July soft red winter wheat contract was down 9-3/4 cents at $6.18 a bushel. K.C. hard red winter wheat futures were down 3.0% and MGEX July spring wheat was off 1.9%.

Wheat futures had showed some strength during the overnight trading session on support from concerns over safe shipment of Black Sea supplies and lower output in Australia.

"There are some supply issues emerging, but U.S. wheat is struggling to find business," said one Singapore-based grain trader.

CBOT July corn futures were up 1/2 cent at $6.08-1/2 a bushel and CBOT July soybean futures were up 15-1/4 cents at $13.68-1/2 a bushel. (Additional reporting by Naveen Thukral in Singapore and Sybille de La Hamaide in Paris; Editing by Rashmi Aich, Subhranshu Sahu and David Gregorio)