* Mid-Atlantic factory activity rebounds in October * Initial jobless claims fall 6,000 last week * Existing home sales fall 3 percent in September * Data consistent with slow growth but not recession By Lucia Mutikani WASHINGTON, Oct 20 (Reuters) - Factory activity in the U.S. Mid-Atlantic region rebounded in October and the number of Americans claiming new jobless benefits fell last week in fresh signs that the economy was likely to duck a new recession. Optimism over the economy was tempered, however, by other data on Thursday showing a drop in sales of previously owned homes and only a small rise in a gauge of future growth. "The numbers we have seen today provide some hints that the domestic economy is doing a little bit better, even with the challenges that are unfolding in Europe," said Michael Strauss, chief economist at Commonfund in Wilton, Connecticut. Initial claims for state unemployment benefits slipped 6,000 to 403,000 last week, the Labor Department said. A four-week average, which smooths out weekly volatility to give a better view of trends, hit its lowest level since April. Separately, the Philadelphia Federal Reserve Bank's business activity index rebounded to 8.7 in October, the highest reading in six months, from minus 17.5 in September. A reading above zero indicates factory activity is expanding in the region, which covers eastern Pennsylvania, southern New Jersey and Delaware. U.S. stocks initially rose on the data, but surrendered most gains on nagging doubts over whether European leaders would decisively deal with the euro zone debt crisis at a summit this weekend. Prices for U.S. Treasury debt were little changed while the dollar was a touch weaker against a basket of currencies . Fears had been mounting that the sickly U.S. economy was heading back toward recession after growth wobbled in the first half of the year and after consumer confidence plunged in August amid signs both the United States and Europe were having trouble coming to terms with their huge debts. But the recent stream of data, including figures on retail sales and trade, suggest output sped up in the third quarter. Analysts estimate U.S. gross domestic product grew at an annual pace of anywhere between 2.3 and 2.7 percent, a sharp step up from the second quarter's tepid 1.3 percent rate. "There is little evidence the economy is ready to enter a downturn based on the Philadelphia Fed (data)," said Joseph LaVorgna, chief U.S. economist at Deutsche Bank in New York.JOBS MARKET TONE IMPROVING That view was also underscored by the four-week moving average of initial jobless claims. The claims data covered the survey week for the government's closely watched nonfarm payrolls count for October. Initial claims dropped 25,000 between the September and October survey periods, suggesting a step-up in nonfarm employment after payrolls increased 103,000 last month. After spiking in mid-September, jobless claims appear to have settled near the 400,000 mark that is usually associated with some improvement in the jobs market. Weak unemployment is a thorny issue for the Federal Reserve, which is weighing further options to boost output and lower the jobless rate after slashing interest rates to near zero and pumping about $2.3 trillion into the economy. On Thursday, St. Louis Fed President James Bullard acknowledged the improved tone in economic data but his counterpart at the Cleveland Fed, Sandra Pianalto, did not believe growth would pick up soon.