* Weak US manufacturing data increases Fed easing hopes * Technical momentum indicator RSI jumps after rally * Gold market eyes ECB decision, US jobs data later in week * Coming up: U.S. factory orders due Tuesday By Frank Tang NEW YORK, July 2 (Reuters) - Spot gold edged up Monday, though futures settled easier, after a report showing an unexpected decline in U.S. manufacturing activity increased bullion's investment appeal. The metal, which fell in the morning on profit-taking, gained ground after the Institute for Supply Management said U.S. manufacturing sector shrank in June for the first time in nearly three years as new orders tumbled. Gold prices have been sensitive to signs of economic weakness, which tend to increase the likelihood of monetary easing by the Federal Reserve. Technical momentum in gold built after Friday's rally on a European deal to shore up banks and cut borrowing costs. The RSI, a closely watched technical indicator, jumped nearly 40 percent on Friday after hovering just above oversold territory in the previous session. Analysts, however, said the metal is likely to continue trading in a tight range between technical resistance and support. "After all the excitement on Friday, and the improvement in technicals, we are still rangebound and are still in the same broad range that we've been in since the beginning of May," said Stanley Dash, vice president of applied technical analysis at TradeStation. Spot gold was up 20 cents at $1,597.19 an ounce by 3 p.m. (1900 GMT), having fallen to a low of $1,586,84. U.S. gold futures for August delivery settled down $6.50 at $1,597.70 an ounce, having closed earlier and higher than bullion on Friday. Trading volume was about half of its 30-day average, preliminary Reuters data showed. PHYSICAL DEMAND LAGS Demand for gold from the world's largest bullion consumer, India, remained lackluster as a recent depreciation in the rupee raised prices for local buyers. The world's largest gold-backed exchange-traded fund (ETF), New York's SPDR Gold Trust, reported a 2.11 tonne outflow on Friday, extending its first quarterly decline in holdings in a year. In addition, money managers cut their net long position in gold futures and options by 20 percent, the first drop in five weeks, as a lack of fresh monetary stimulus by the U.S. Federal Reserve prompted some investors to reduce bullish bets. Among other precious metals, silver edged up 0.2 percent to $27.54 an ounce. Spot platinum gained 0.4 percent at $1,448.10 an ounce, while spot palladium fell 1.1 percent at $571.55 an ounce.