CHICAGO, Jan 17 (Reuters) - Chicago Board of Trade (CBOT) corn and soybean futures rallied to multi-month highs on Tuesday as signs of export demand and follow-through support from last week's bullish U.S. government supply/demand reports overshadowed early pressure from wetter South American weather forecasts, traders said.

Wheat followed the higher trend.

CBOT March corn settled up 10-1/4 cents at $6.85-1/4 per bushel after reaching $6.87, its highest level since Nov. 4. March soybeans ended up 12 cents at $15.39-3/4 a bushel after rising to $15.41, the contract's highest level since mid-June. March wheat finished up 8 cents at $7.51-3/4 a bushel.

Technical buying accelerated in corn as the March contract pushed above its 200-day moving average near $6.78.

The markets got a boost after the U.S. Department of Agriculture (USDA) confirmed private sales of 150,000 tonnes of U.S. corn to Colombia and 119,000 tonnes of soybeans to unknown destinations.

Weekly export inspections data also lent support, with the USDA reporting 774,461 tonnes of U.S. corn and 2.075 million tonnes of soybeans inspected for export in the latest week, both above a range of trade expectations.

Futures rallied from early declines tied to weekend rains in Brazil's crop belt and forecasts for much-needed showers in Argentina's crop belt.

"We've had those (weather forecasts) come out and then not materialize. Until we see an end to some of the dryness down there, (traders) are going to be supporting this market," said Sherman Newlin, an analyst with Risk Management Commodities.

Traders continue to digest the USDA's Jan. 12 stocks and supply/demand reports that showed smaller-than-expected U.S. grain supplies as of Dec. 1.

"Fund managers jumped back on the bandwagon of buyers that received support from Thursday's USDA ... crop report," StoneX chief commodities economist Arlan Suderman wrote in a client note. "That rally seemed to lack conviction on Friday ahead of the three-day holiday weekend, resulting in the overnight selling, but the buying returned today."

Remarks by Russian President Vladimir Putin that his country should maintain stocks and not export all its agricultural supplies drew attention to geopolitical risks as Russia's invasion of Ukraine continues.

Meanwhile, Algeria's state grains agency OAIC bought milling wheat in an international tender, with quantities estimated in initial assessments by European traders at 510,000 tonnes to 600,000 tonnes. (Reporting by Julie Ingwersen; Editing by Andrea Ricci and Leslie Adler)