SINGAPORE, Aug 2 (Reuters) - Chicago wheat futures rose for the first time in six sessions on Wednesday, underpinned by concerns over a lack of Ukrainian grains, although supplies from freshly harvested U.S. crop limited the upside potential in prices.

Soybeans rose for a second session on optimism over strong demand.

FUNDAMENTALS

* The most-active wheat contract on the Chicago Board of Trade (CBOT) rose 1.4% to $6.61-1/4 a bushel, as of 0031 GMT, having hit its weakest since July 18 at $6.43 in the last session.

* Soybeans climbed 0.5% to $13.47-1/4 a bushel and corn gained 0.8% at $5.11-1/4 a bushel.

* The wheat market is being supported by the collapse of a wartime deal allowing Ukrainian sea exports amid attacks on ports, which revived fears of disruption to massive Black Sea grain trade.

* However, the United States has been told that Russia is prepared to return to talks on a deal that had allowed the safe Black Sea export of Ukraine grain, but "we haven't seen any evidence of that yet," the U.S. envoy to the United Nations said on Tuesday.

* The U.S. Department of Agriculture's weekly crop report on Monday showed that the U.S. winter wheat harvest was in its latter stages, providing much-needed milling wheat to the market.

* The soybean market was monitoring U.S. export activity after an increase in the volume of weekly port inspections and the announcement of sales of 132,000 metric tonnes of soybeans to China on Monday.

* U.S. soybean crushers processed 174.5 million bushels of soybeans in June, the U.S. Department of Agriculture said, below analyst expectations of 175.5 million bushels.

* Farmers in Brazil, the world's biggest soybean supplier, will set another production record in the next growing season, consultancy StoneX said on Tuesday in its first estimate for the 2023/24 harvest year.

* Brazil's soybean output will grow by an estimated 3.7% to 163.5 million metric tonnes as farmers are expected to plant a larger area. In the previous cycle, growers reaped an estimated 157.7 million metric tonnes, which was also a record, StoneX said.

* Commodity funds were net sellers of CBOT corn futures contracts on Tuesday, and net even in soybean, soyoil and soymeal futures contracts, traders said. Traders' estimates of fund activity in soybeans ranged widely from net sales of 5,000 contracts to net purchases of 5,000 contracts.

MARKET NEWS

* Most global stocks dipped, while oil prices fell and Treasury yields climbed, as investors weighed declining factory activity in the euro zone and China with stabilising U.S. manufacturing and job openings that signalled a still-tight labour market.

DATA/EVENTS (GMT) 1215 US ADP National Employment July (Reporting by Naveen Thukral; Editing by Subhranshu Sahu)