CHICAGO, June 6 (Reuters) - U.S. corn futures rose on Tuesday as investors unwound bearish bets ahead of a key government supply and demand report at the end of the week, traders said.

"It is all money flow," said Karl Setzer, brokerage research lead with Mid-Co Commodities. "When you get down to it, funds have built a huge short position in corn ... and we are starting to see quite a little bit of short-covering ahead of the U.S. Agriculture Department's World Agricultural Supply and Demand Estimates report."

Soybeans also closed strong after trading in both positive and negative territory during the session. Prices peaked at their highest in nearly three weeks.

Wheat futures were mixed, with the most-active Chicago Board of Trade soft red winter wheat contracts firming on a technical bounce.

But K.C. hard red winter wheat and MGEX spring wheat contracts sank as export demand for U.S. supplies remained slim despite concerns about escalations in the Ukraine-Russia war disrupting shipments from those two key global suppliers.

The benchmark Chicago Board of Trade July soft red winter wheat contract settled up 3-3/4 cents at $6.27-3/4 a bushel.

The lowest offer presented at an Egyptian state purchasing tender for wheat on Tuesday was $229 per tonne for 55,000 tonnes of Russian wheat on a free-on-board basis, traders said. No U.S. wheat was offered in the tender.

"Russian prices are still moving south. They have got a huge carryover from last year and everything looks like they will have a more than ample new crop," said Tom Fritz, a partner with EFG Group in Chicago. "World wheat prices just don't let us rally.

CBOT July corn futures were up 10-1/2 cents at $6.08 a bushel and CBOT July soybeans were 3-1/4 cents higher at $13.53-1/4 a bushel after peaking at $13.64, their highest since May 17.

Private exporters reported the sale of 165,000 tonnes of soybeans for shipment to Spain in the 2022/23 marketing year, the U.S. Agriculture Department said on Tuesday morning. (Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Marguerita Choy and Richard Chang)