* Milder U.S. weather expected, following heat wave

* CBOT soybeans hit lowest price since July 13

* No further major attacks on Ukraine's grain system

CHICAGO, July 31 (Reuters) - Chicago soybeans and corn fell on Monday, pressured by expectations of cooler, wetter weather across the U.S. Midwest in August.

Wheat also dropped, despite worries over Black Sea supplies, although no new major Russian attacks on Ukrainian grain infrastructure were reported over the weekend.

Chicago Board of Trade most-active corn fell 18 cents to $5.12-1/4 a bushel by 11:15 a.m. (1615 GMT), its fifth consecutive decline.

Soybeans lost 47 cents to $13.35-1/2 a bushel, their lowest since July 13, while wheat dropped 40-1/4 cents to $6.64 a bushel.

Cooler temperatures and increased rain forecasts are expected to bolster crop development, adding pressure to markets.

"Some of the dryer spots of Iowa and Minnesota are expecting rain this week," said Ed Duggan, senior risk management specialist at Top Third Ag Marketing. "The extended forecast, for August, they’ve taken all the heat out."

The U.S. Department of Agriculture (USDA) is expected to lower weekly condition ratings for U.S. corn and soybean crops later on Monday following recent heat.

The USDA reported sales of 132,000 metric tons of U.S. soybeans to China for shipment in the 2023/24 season. The agency also reported sales of 183,300 tons of soymeal to the Philippines.

"Last week was a big week for purchases of beans. If that continues, that could be another supportive factor," said Chuck Shelby, president of Risk Management Commodities. "This market is looking for export business. If we start to see that come back around on a big break, that would be a positive."

Traders continue monitoring the war in Ukraine after Russia in July left Ukraine's safe export shipping agreement and attacked Ukrainian grain export ports and infrastructure for Ukraine’s exports via the European Union along the Danube. (Reporting by Christopher Walljasper in Chicago; Additional reporting by Naveen Thukral in Singapore and Michael Hogan in Hamburg Editing by Mark Potter)