* Two-year note yield rises near 3-1/2 month highs * U.S. jobless claims fell in latest week * Treasuries on track for 2nd worst year since 1996 -BAML By Richard Leong NEW YORK, Dec 26 (Reuters) - U.S. benchmark Treasuries yields edged higher on Thursday, just below their two-year high of 3 percent, in light trading as most investors stayed out of the market after the Christmas holiday. The U.S. bond market reopened after being closed on Wednesday, while major European markets stayed shut, keeping volume well below average. Treasuries yields approached peaks set in September after the Federal Reserve said last week it will shrink its monthly purchases of Treasuries and mortgage-backed securities by $10 billion, to $75 billion, in January. If the 10-year Treasury yield, a benchmark for mortgage rates and investment returns, were to rise much above 3 percent, it might be a negative for stocks and other risky assets. A further rise in bond yields would push up long-term borrowing costs, taking steam out of the economic recovery - similar to what happened this past summer, analysts said. "Other markets will take notice if we establish a foothold above 3 percent," said Rob Zukowski, senior technical analyst at 4Cast Ltd in New York. The rise in yields this year has hurt the Treasuries market, which is on course for its second worst year since 1996, according to data from Bank of America Merrill Lynch. Given the thin year-end volume, Zukowski said, the few investors who have not closed their books for the year are unlikely to make any big trades even if the 10-year yield strays above 3 percent. Investors await the next set of government payrolls figures and whether they indicate the recent strength in the economy is sustainable, allowing the Fed to taper further, analysts said. "The proof in the pudding is the next employment report," said Wilmer Stith, who co-manages the Wilmington Broad Market Bond Fund in Baltimore. "The economy is on a slow simmer." Moreover, Treasuries prices do not have near daily support from the Fed's purchases for its third round of quantitative easing. The U.S. central bank will not resume buying U.S. government debt until early 2014. Fed policymakers opted to dial back their bond purchases on signs of economic improvement although unemployment has remained relatively high and inflation has been stuck below their 2 percent target. The Labor Department said on Thursday first-time filings for unemployment benefits totaled 338,000 in the week ended Dec. 21, down from an upwardly revised 380,000 the previous week. The larger-than-expected decline buttressed the view that the domestic labor market has further improved, but it was not enough to support the notion that job growth is speeding up, boosting economic growth and inflation from current levels. This latest level of weekly jobless claims has coincided with monthly job creation rising to the 200,000 area and the unemployment rate falling to a five-year low of 7.0 percent in November. "If we get another month of 200,000-plus in payrolls and the unemployment rate with a six (percent)-handle, we could see further deterioration in the 10-year yield," Stith said. If the upcoming jobs readings disappoint, the 10-year yield might fall back to 2.75 percent, he added. The December payrolls data will be released on Jan. 10. Benchmark 10-year Treasury notes fell 2/32 in price to yield 2.992 percent, up one basis point from late on Tuesday. The 10-year yield touched 3 percent overnight, fractionally below a two-year intraday high set on Sept. 6, according to Reuters data. The yield on two-year notes was up one basis point at 0.415 percent, above its 50-day moving average but still below the intraday high of 0.538 percent in September. Thirty-year bonds fell 14/32 in price, yielding 3.921 percent, up 2.1 basis points from late on Tuesday. The 30-year yield was less than seven basis points below the two-year high, which was set more than three months ago. Barring a massive rally between now and next Tuesday, the Treasuries market will suffer its second biggest annual loss in 17 years. The Bank of America Merrill Lynch's Treasuries index has fallen 3.3 percent year-to-date, which is slightly smaller than the 3.5 percent drop in 2009.