CHICAGO, May 24 (Reuters) - U.S. wheat futures fell on Wednesday on a round of profit-taking as traders said the market lacked fundamental inputs to drive prices higher a day after a rally driven by renewed concerns over a Black Sea deal.

Corn futures were firm for the second day in a row, with old-crop contracts leading the way on signs of strength in the cash market. Deferred corn contracts ended higher but closed below session peaks after updated weather forecasts called for rain in Iowa within the next week.

The soybean market was mixed as old-crop contracts edged higher on technical buying while deferred contracts eased on demand concerns.

Wheat futures surged 2.6% on Monday but ample supplies in Russia - underscored by falling prices, a planned revision of its export tax, and favourable harvest prospects - continued to cap wheat prices, traders said.

"There has not been any demand," said Scott Harms, agricultural risk specialist at Archer Financial Services. "We just do not have a home for U.S. wheat."

Chicago Board of Trade July soft red winter wheat settled down 16 cents at $6.06-1/4 a bushel.

On Tuesday, Ukraine accused Russia of effectively cutting the Ukrainian port of Pivdennyi out of a deal allowing safe Black Sea grain exports of food and fertiliser from Ukrainian ports of Odesa, Chornomorsk and Pivdennyi. Russia complained it had been unable to export ammonia via a pipeline to Pivdennyi.

In China, a surplus of cheap wheat is curbing consumption of both corn and soymeal, according to feed makers and analysts.

A firm dollar and financial market weakness, as investors fretted about stalled talks to raise a U.S. government debt ceiling, further weighed on sentiment, traders said.

CBOT July corn futures were up 9-3/4 cents at $5.87-1/4 a bushel.

CBOT July soybeans gained 2 cents a $13.24-1/2 a bushel. New-crop November dropped 2-3/4 cents to $11.85 a bushel. (Additional reporting by Gus Trompiz in Paris and Matthew Chye in Singapore; Editing by Sherry Jacob-Phillips, Christina Fincher and David Gregorio)