* World, US corn stocks smaller than traders expected * Lowest US corn stocks in 17 years, equaling 3-week supply * USDA cuts Australia wheat crop 12 pct, Russia 3 pct * US headed for smallest corn exports in 37 years * Corn futures up 5 pct, wheat up 2 pct on USDA data By Charles Abbott WASHINGTON, Oct 11 (Reuters) - U.S. and world corn stocks will be tighter than expected well into 2013 and drought has cut the wheat crop in leading exporter Australia, the U.S. government forecast, driving up futures as world farm ministers prepare to meet on high food prices. It was the second time in two weeks the Agriculture Department surprised the markets with smaller-than-expected estimates of stocks. This time, the USDA said unrelenting demand would pull U.S. corn and soybean stocks to the lowest levels in years - 17 years for corn and eight for soybeans. Agriculture ministers are due to meet next week in Rome amid renewed fears of a crisis in food supplies exacerbated by the worst U.S. drought in more than 50 years. The USDA's updated forecast of world crops, including a downturn in corn and wheat stocks, could be the latest and most comprehensive guidepost for the meeting. Corn futures soared 5 percent on the news, hitting a three-week high. Wheat futures were up 2 percent near the close of the trading day in Chicago. Soybeans were up 1.6 percent. While at high levels, corn is about 10 percent lower and soybeans 15 percent lower than records set during the summer. "The ending stocks numbers were all that matters," said Mike Zuzolo, of Global Commodity Analytics. "The heart of the matter is we are running too tight on supplies, and this should get the end-users to pick up the pace on purchasing their needs for the first quarter."