* Hopes for milder U.S. weather following heat wave

* No further major attacks on Ukraine's grain system

(Adds continued price weakness in European trade)

SINGAPORE/HAMBURG, July 31 (Reuters) - Chicago wheat, corn and soybeans fell on Monday as forecasts of milder weather in the U.S. Midwest grain belt reduced concerns over heat damage to U.S. crops.

Wheat dropped despite worries over Black Sea supplies, with relief there were no reports of major Russian attacks on Ukrainian grain infrastructure over the weekend.

"U.S. weather is driving corn and soybeans lower," said one Singapore-based trader. "Wheat prices have dropped below $7 a bushel, but the supply situation for wheat is still uncertain. Any further escalation in the Russia-Ukraine war can drive prices higher."

Chicago Board of Trade most active wheat fell 2.6% to $6.85-1/2 a bushel at 1014 GMT with European Euronext September wheat also down 2.3%. Chicago corn fell 1.9% to $5.19-3/4 a bushel, soybeans fell 1.7% to $13.58-1/4 a bushel.

Forecasts of cooler weather, welcome for crops in the U.S. Midwest, pushed prices lower. But some traders expect the U.S. Department of Agriculture (USDA) to lower weekly condition ratings for U.S. corn and soybean crops in a report later on Monday following recent heat.

Traders are monitoring the war in Ukraine after Russia earlier in July left Ukraine's safe export shipping agreement and attacked Ukrainian grain export ports and infrastructure for Ukraine’s exports via the EU along the Danube.

"The big question now is how will Ukraine be able to ship its exports out without its safe shipping channel and will Russia leave Ukraine's grain infrastructure alone," one German trader said. "Meanwhile, large volumes of Russian wheat look like being available to importers with estimates of the size of Russia's crop this summer being increased."

Following recent price falls, traders noted a tender on Monday from Algeria - the first major wheat import tender from a major Middle East/North African buyer since Russia left Ukraine’s safe shipping deal. (Reporting by Naveen Thukral in Singapore and Michael Hogan in Hamburg; Editing by Subhranshu Sahu, Sherry Jacob-Phillips and Christina Fincher)