* Soybean futures fall amid forecast of greater supply, weak demand

* Wheat futures boosted by Black Sea strike; corn also higher

NEW YORK, Sept 13 (Reuters) - Soybean futures on the Chicago Board of Trade (CBOT) slid for a second straight session on Wednesday on weak demand, while wheat climbed further from the prior day's 33-month low following reports that Ukrainian grain exports dropped sharply.

The benchmark November soybean contract was down 0.2% at $13.44 per bushel by 1636 GMT, near a three-week low.

"Our demand right now isn't great," said Mark Schultz, chief analyst at NorthStar in Minneapolis, citing a mix of factors.

"Speculative traders long this stuff are getting out of the market. And there have been no big (export sales) purchases announced in the daily reporting," he said.

Beans took a hit after the U.S. Department of Agriculture (USDA) on Tuesday forecast a drop in U.S. soy production, but not as big a cut as some analysts had expected. Schultz said soybean prices may find support if damage to the crop from a dry, hot summer turned out to be greater than expected.

"I think it's still iffy whether the harvest gets better or worse. I think the bean likely is smaller, because of rainfall," he said.

CBOT wheat futures rose on rising hostilities in the Black Sea breadbasket region as Ukraine claimed it struck a Russian naval base in Crimea.

Kyiv said on Wednesday more than 100 of its port facilities had been damaged by Russian bombardment and its grain exports were down sharply since Moscow withdrew from a wartime grain shipping deal.

The benchmark December wheat contract traded at $5.95-3/4 a bushel, up 1.4%.

Corn futures followed wheat higher in a rebound from recent multi-year lows, with December futures up 1.2% at $4.82-1/2 a bushel. Gains were capped by stiff export market competition from a record Brazilian crop and USDA's forecast on Tuesday of a larger-than-expected U.S. harvest.

(Reporting by Zachary Goelman;Editing by Elaine Hardcastle)