CHICAGO, Jan 15 (Reuters) - U.S. wheat futures rose on Friday, supported by Russia's plan to double its tax on exports of the grain, while corn and soybeans fell as traders took money out of the market following their surge to multi-year highs earlier in the week.

Wheat traded both sides of unchanged, ending in positive territory but well below the day's peaks after hitting its highest level since 2014 overnight. Traders said leading world supplier Russia's tax plans fanned concerns about reduced global availability.

"This is going to reduce Russian exports," said Nathan Cordier of consultancy Agritel. "The response of the market is in a way to stifle demand (with high prices)."

CBOT March soft red winter wheat settled 5-1/2 cents higher at $6.75-1/2 a bushel. The most-active contract peaked at $6.93 overnight, its highest since May 2014.

K.C. March hard red winter wheat was up 7-3/4 cents at $6.44-1/4 a bushel. K.C. futures, which track the crop that makes up the bulk of U.S. exports, hit overnight their highest since December 2014.

Russia plans to impose a wheat export tax of 50 euros a tonne from March 1, increasing an initial 25 euro levy due to apply from Feb. 15, its economy minister said on Friday, in another push to cool domestic food prices.

CBOT March corn futures were down 2-3/4 cents at $5.31-1/2 a bushel and CBOT March soybeans dropped 13-3/4 cents to $14.16-3/4 a bushel.

The U.S. Department of Agriculture's reduced forecasts for U.S. corn and soybean supplies on Tuesday sparked a rally that pushed soybeans to a 6-1/2-year high and corn to a 7-1/2-year high.

But the market was waiting for more bullish news before driving prices above those levels.

"We pulled back from the spike highs," said Matthew Wiegand, broker at FuturesOne. "We are just kind of drifting." (Additional reporting by Gus Trompiz in Paris and Naveen Thukral in Singapore; Editing by Louise Heavens, Dan Grebler and Paul Simao)