* Forecasts of U.S. rains pressure corn, soybeans

* Wheat stays weak with focus on Russian export competition

PARIS/SINGAPORE, June 28 (Reuters) - Chicago corn and soybean futures lost ground on Wednesday to touch one-month lows as forecasts of significant rainfall in parched U.S. Midwest crop belts removed a weather premium that boosted prices earlier in June.

Wheat tracked corn lower, further pressured by export competition from Russia and the start of northern hemisphere harvests, traders said.

Grain markets were also looking ahead to U.S. government planting and stocks estimates on Friday.

Weather projections show widespread showers in the Midwest in the coming two weeks, which may help corn and soy plants recover from drought before crucial summer growth phases.

The rain prospects have turned attention away from U.S. government data on Monday showing the worst corn and soybean soybean crop conditions in decades.

"It seems that funds have begun to exit their recently established long positions in corn and soybeans on increased chances of improved soil moisture in the U.S. Midwest," brokerage Copenhagen Merchants said in a note.

Expectations of record corn and soybean production in Brazil and tepid export demand for U.S. supplies have also tempered worries about Midwest growing conditions.

The most-active corn contract on the Chicago Board of Trade (CBOT) was down 2.3% at $5.48 a bushel by 1145 GMT, after earlier reaching its lowest since May 18.

CBOT soybeans fell 1.6% to $12.74-1/4 a bushel, after dropping earlier to its weakest since May 31.

CBOT wheat gave up 1.2% to $6.90-1/2 a bushel after touching a new one-week low.

The wheat market has shifted its focus back to ample supplies, after jitters caused by last weekend's aborted mutiny by the Wagner militia in Russia, the world's top exporter.

"Wheat also faces additional pressure from easing concerns over Russia political instability," Reilly said.

The European Union's crop monitoring service MARS on Monday forecast Russia's wheat production this year at 86.7 million metric tons, underlining expectations for an above-average crop. (Reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Rashmi Aich, Subhranshu Sahu and Barbara Lewis)