* European stocks dip, dollar index near 3-month highs
* Chinese demand weak over holiday, premiums unchanged (Releads, updates prices, adds comment)
By Clara Denina
LONDON, June 3 (Reuters) - Gold fell to a four-month low on Tuesday, on course for a six-day losing streak after upbeat U.S. data kept the dollar close to a multi-month high versus a basket of currencies, offsetting the positive impact on the metal of lower equities markets.
New orders for U.S. factory goods rose for a third straight month in April, pointing to strength in manufacturing and the broader economy.
Spot gold, initially firmer, hit its lowest since Feb. 3 at $1,240.61 an ounce in earlier trade. It was down 0.1 percent at $1,242.60 an ounce by 1439 GMT. Prices are on track for their longest losing streak in nearly seven months.
U.S. gold futures for June delivery were down $2.40 an ounce at $1,241.80 an ounce.
"The market is not finding any confidence at the moment, and you could even argue that now we have seen a couple of attempts to bounce but those have been very shallow, which leaves the risk that we could see further weakness in the market," Saxo Bank senior manager Ole Hansen said.
Global shares fell and the dollar index eased 0.1 percent but remained near its highest since Feb. 13, as investors digested data showing that euro zone price inflation unexpectedly dropped in May, increasing the risks of deflation in the currency area and sealing the case for the European Central Bank to act this week.
The ECB meets on Thursday and is widely expected to cut interest rates, including lowering the rate banks are charged for depositing funds with the central bank to below zero.
"There is a fear in the gold market that as various positive macro events come together they can give gold a severe blow and this time around the Chinese demand is not going to be there," Macquarie analyst Matthew Turner said.
In other markets, U.S. 10-year Treasury yields rose to around 2.56 percent, boosted by positive U.S. economic numbers. Returns on U.S. bonds are closely watched by the gold market, given that the metal pays no interest.
Weak demand in top consumer China contributed to keeping prices near their lows, with buying interest failing to come back strongly after the Dragon Boat festival on Monday.
Prices for 99.99 percent purity gold on the Shanghai Gold Exchange eased on Tuesday. Premiums to the global benchmark failed to budge on Tuesday, remaining at about $3 an ounce - the same level as Friday's.
Among other precious metals, platinum was down 0.3 at $1,424.74 an ounce and palladium rose 0.7 percent to $833 an ounce, with wage strikes in major producer South Africa dragging on for a fifth month.
South Africa's Association of Mineworkers and Construction Union (AMCU) is considering a government proposal to resolve the strike and will table it to its members this week, union president Joseph Mathunjwa said on Tuesday.
Silver was down 0.1 percent at $18.73 an ounce. (Additional reporting by A. Ananthalakshmi in Singapore; Editing by David Evans and Susan Thomas)