* U.S. stocks fall, European stocks extend losses * Weak earnings, Deutsche loss, German retail sales weigh * Euro climbs for a third straight day NEW YORK, Jan 31 (Reuters) - The euro gained on Thursday for the third straight session against the dollar on the way to its best monthly performance in more than a year, while U.S. stocks fell as investors awaited a key U.S. jobs report slated for Friday. U.S. data continued to paint a mixed picture of the world's largest economy. A measure of business activity in the U.S. Midwest rose in January to its strongest since April, but an earlier report indicated a rise in U.S. jobless claims in the latest week. A drop in German retail sales initially pressured the euro, but the currency's recent bullish trend resumed during U.S. trading. The single currency was headed for its best month in 15 months against the dollar, as signs of recovery in the euro zone's economy and its banks helped the euro. The euro hit a peak of $1.3593 on Thursday before paring gains. The Federal Reserve's promise of continued support was widely expected to keep downward pressure on the dollar. The euro zone common currency was last at $1.3570 and up 2.9 percent this month against the dollar, its best month since October 2011. The dollar, meanwhile, touched a fresh 2-1/2 year high against the yen. "The overall recent trends are intact," said Nick Bennenbroek, head of currency strategy, at Wells Fargo Bank in New York. "The euro probably wants to go higher and the yen probably wants to go lower." Recent gains in risky assets such as equities, commodities, and high-yield debt have eased after sharp advances in the last six months. Growth in emerging economies such as China has picked up and fears of a collapse of the euro have been calmed by the European Central Bank. Data on Wednesday showed U.S. GDP slipped 0.1 percent where a rise had been expected, although the Federal Reserve indicated the pullback was likely to be brief and repeated its promise to continue supporting the economy. But the main focus is on U.S. payrolls data on Friday for a take on the health of the world's biggest economy. Employers are forecast to have added 160,000 jobs in January after a rise of 155,000 in December. "Unfortunately it's still a mixed picture. It appears we are just getting a lot of conflicting data right now," said Jack Ablin, chief investment officer at BMO Private Bank in Chicago. "With 1,500 (in the S&P stock index) right here, my guess is there is just not enough conviction to push us substantially higher yet." The Dow Jones industrial average was down 49.84 points, or 0.36 percent, at 13,860.58. The Standard & Poor's 500 Index was down 3.85 points, or 0.26 percent, at 1,498.11. The Nasdaq Composite Index was down 0.18 points, or 0.01 percent, at 3,142.13. The S&P 500 is up 5.1 percent this month, its best month since October 2011 and its best January since 1997, using Reuters data. EUROPE SUFFERS The pan-European FTSEurofirst 300 was down 0.6 percent, with the MSCI world index down 0.2 percent. Disappointing results from heavyweights AstraZeneca and Royal Dutch Shell also took their toll on market sentiment. Falling German retail sales, stagnant French consumer spending and a big quarterly loss at Deutsche Bank dashed hopes of a rebound for European shares, which had their biggest daily fall of the year on Wednesday. Those stocks are still up 3.7 percent this month. Spot gold drifted down to $1,660.40 an ounce after hitting a one-week high on Wednesday. German Bund futures pared gains on Thursday, continuing a recent shift away from safe-haven debt. Bund futures were last 40 ticks higher on the day at 141.83, having risen as high as 142.17. Prices for U.S. Treasuries were volatile a day after the Fed said it would continue buying bonds as the economy temporarily stalled, but uncertainty about growth in the world's biggest economy kept yields within recent ranges. The benchmark 10-year U.S. Treasury note was up 2/32, with the yield at 1.9831 percent.