* Global shares hit highest level since September * Wall St extends rally on 'fiscal cliff' hopes * Euro hits fresh 7-1/2-month high vs U.S. dollar By Angela Moon NEW YORK, Dec 18 (Reuters) - Global stocks advanced to their highest levels since September on Tuesday on signs of compromise in U.S. talks to stop automatic tax hikes and spending cuts that could hurt the economy next year. With confidence rising that lawmakers would avert the "fiscal cliff," investors shifted funds to stocks and the euro and pulled away from assets traditionally viewed as safe harbors like bonds, gold and the U.S. dollar. The euro hit a 7-1/2 month high against the greenback while gold fell almost 2 percent on to its lowest since August. Wall Street rallied, putting the S&P 500 on track for its best two-day run in a month, as investors gained confidence that federal budget talks were progressing, even as significant differences separated Democrats and Republicans in Washington. The gains followed a rally on Monday that lifted the S&P 500 to its highest point in nearly two months. Investors remain confident Washington will come to an agreement. President Barack Obama's most recent offer makes concessions to the Republicans on taxes and entitlement spending, but House Speaker John Boehner said the offer is "not there yet," though he remains hopeful of an agreement. Senate Democrats have expressed concern about entitlement cuts, particularly to Social Security. "Agreement on the 'fiscal cliff' could bring a significant move away from safe-haven assets, not just here in the U.S., but globally," said Dan Heckman, senior fixed income strategist at U.S. Bank Wealth Management in Minneapolis. For a second day, banks led the rally on Wall Street. Goldman Sachs Group was up 2.8 percent and Morgan Stanley gained 2.3 percent after Jefferies Group reported a higher-than-expected adjusted quarterly profit. Jefferies was up 3 percent to $18.79. The S&P 500 Financial Index climbed 1 percent. The Dow Jones industrial average was up 84.56 points, or 0.64 percent, at 13,319.95. The Standard & Poor's 500 Index was up 11.04 points, or 0.77 percent, at 1,441.40. The Nasdaq Composite Index was up 29.80 points, or 0.99 percent, at 3,040.40. European shares ended higher, with a key index closing just a few points below its 2012 high. The euro surged to its highest level against the dollar in more than seven months and held close to a nine-month peak versus the yen on Tuesday. The euro was last up 0.5 percent at $1.3228 after hitting a high of $1.3238, its strongest level since early May. The dollar index fell to a two-month trough of 79.260. The index was last quoted at 79.318, down 0.3 percent. Oil prices rose. Front-month Brent crude oil prices rose $1.28 to $108.94 a barrel by 3:06 p.m. (2006 GMT). U.S. January crude rose 73 cents, or 0.84 percent, to settle at $87.93 a barrel, having traded from $87.21 to $88.16. In other assets, gold, seen as a safe-haven asset, tumbled with spot gold down 1.9 percent at $1,666.90 an ounce. U.S. Treasury yields rose to their highest since October on Tuesday. The benchmark 10-year U.S. Treasury note was down 15/32, with the yield at 1.824 percent.