MOSCOW, June 16 (Reuters) - Russia's seaborne grain exports rose 71.7% year-on-year to 3.7 million metric tons in May, according to shipping data from industry sources released on Tuesday.

Total seaborne exports have reached 49.8 million tons so far this season, 10.5% up year-on-year, according to the data.

Exports via the Black Sea route, the main channel for Russian grain exports, increased by 59.5% to 3.1 million tons in May.

Shipments via the Caspian Sea, primarily to Iran, rose to 0.3 million tons, while exports via Baltic Sea terminals, which supply Russian grain to new markets including Africa and Latin America, jumped by 72.0% to 0.1 million tons.

Supplies via Far East terminals increased by 37% to 0.1 million tons in May.

(Reporting by Gleb Stolyarov; Editing by Mark Trevelyan)