NEW YORK, Oct 5 (Reuters) - Chicago wheat futures rallied on Thursday, boosted more than 3% higher on reports of new tensions in the Black Sea region.

Corn futures hit a one-month peak, breaking out of a recent range holding above a key technical level, and soybeans rose modestly despite lackluster export demand.

A Turkish-flagged general cargo ship hit a mine on Thursday in the Black Sea off the coast of Romania and sustained minor damage but the crew was safe, maritime and security sources said.

The Black Sea area has been listed as a high risk zone by insurers and floating mines remain a peril.

"It looks like the relentless downtrend due to perceptions that Ukraine could move its grain out the door by sea has hit a hiccup," Charlie Sernatinger, an analyst at Marex Capital, said in a note to clients.

Chicago Board of Trade (CBOT) wheat, which hit a three-year low last week, climbed more than 3% to settle at $5.78-1/4 a bushel.

The move up put December wheat 1-1/2 cents below its 20-day moving average, a level where prices met sustained technical resistance at every test since early August.

Corn prices saw a similar rally, climbing to their highest levels in more than a month to settle at $4.97-1/2, its highest closing price since Aug. 8.

The contract crossed back above its 50-day moving average for the first time since July 27, a milestone that may have propelled it higher before the settlement.

"That kind of caused a lot of snowball activity in the buying interest and so here we are, up 11 cents, looking pretty darn strong, Pope said.

The rallies in corn and wheat supported gains in the soybean market, but gains were kept in check by reports of better-than-expected yields from the U.S. harvest.

CBOT November soybeans settled up 7-3/4 cents at $12.80-3/4 a bushel. (Reporting by Zachary Goelman in New York City; additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Elaine Hardcastle and Marguerita Choy)