* Greek debt tension threatens rally in risk assets * Global stocks could fall for the first session in five By Rodrigo Campos NEW YORK, Feb 6 (Reuters) - Concern that Greece might not accept the terms of a proposed new bailout deal brought a rally in global shares to a halt on Monday, while the euro pared earlier losses as some shorts covered their bets. U.S. stocks edged lower, tracking European equities, while a gauge of global shares dipped slightly after four straight sessions of gains. Declines were not enough to derail an uptrend of five consecutive weeks of gains on both the U.S. benchmark S&P 500 index and global stocks measured by MSCI. So far this year, the S&P is up 6.8 percent and global stocks have gained 8.6 percent. The Greek debt crisis remained a concern to markets as political leaders had not agreed to accept unpopular public wage cuts and other measures to qualify for a new bailout from the European Union and the International Monetary Fund. Greece needs the cash by March to meet big debt repayments and avoid an unruly default. The slow progress to sort out Greece's cash problems has angered the country's European partners and undermined investor confidence across markets. "We've had an ultra-strong move, and I think it would be prudent to take some hedges to protect yourself," said Randy Bateman, chief investment officer of Huntington Asset Management in Columbus, Ohio. "There will be more negativity if the (Greek) deal doesn't go through." In afternoon trading in New York, the Dow Jones industrial average dropped 41.81 points, or 0.33 percent, to 12,820.42. The S&P 500 Index fell 2.80 points, or 0.21 percent, to 1,342.10. The Nasdaq Composite lost 6.50 points, or 0.22 percent, to 2,899.16. The FTSEurofirst 300 index of top European shares closed down 0.14 percent. Global stocks measured by MSCI dipped less than 0.1 percent. The euro pared some losses as its earlier decline reached key technical levels, prompting investors to cover their short positions. The single currency fell to a low of $1.3026 according to Reuters data and was last down 0.2 percent at $1.3125. "Headlines out of Europe are affecting sentiment on the euro. Earlier, we had hit stop losses in the euro and we saw it trim some losses. But it's more of the same," said Brian Dolan, chief currency strategist at Forex.com, as investors still awaited the outcome on Greece's debt deal. The underlying sentiment in markets remained positive due to strong January economic data from the United States, China and Germany. An easier monetary stance from the world's major central banks that appears set to continue at key meetings this week also supports investor sentiment. Data on German industrial goods orders, released on Monday, extended the run of good data. A better-than-expected 1.7 percent rise for December was propelled by demand from outside the euro zone, which more than made up for a drop in orders from within the currency bloc. U.S. Treasuries prices edged higher highlighting the safe-haven appeal of U.S. debt. In light, choppy trading, the benchmark 10-year U.S. Treasury note was up 8/32, with the yield at 1.896 percent.