* MSCI world share index down after weak China data
* S&P 500 down slightly after US services data
* European shares edge up, safe-haven bonds make ground
NEW YORK, Jan 6 (Reuters) - A global stock index dipped on Monday after data showed weak service sector growth in China and the United States, while gold edged up to its highest in nearly three weeks.
U.S. Treasuries prices extended gains after the services data, which showed a private index of U.S. service industry activity unexpectedly fell in December.
Earlier, figures showing that China's services sector growth slowed sharply last month added to a stack of disappointing data from the world's second largest economy over the last week.
MSCI's world stock index, which tracks 45 countries, was down 0.2 percent, while the S&P 500 fell slightly after the services data.
The Dow Jones industrial average rose 3.41 points or 0.02 percent, to 16,473.4, the S&P 500 lost 0.62 points or 0.03 percent, to 1,830.75 and the Nasdaq Composite dropped 14.676 points or 0.36 percent, to 4,117.23.
Traders are still second-guessing the Federal Reserve's take on economic data and how it might alter the U.S. central bank's plan to withdraw its quantitative easing stimulus, said Peter Jankovskis, co-chief investment officer at OakBrook Investments in Lisle, Illinois.
"On balance today's data is not going to raise concerns the Fed may accelerate the taper," he said.
Wednesday's December Fed meeting minutes and Friday's non-farm payrolls data could determine stocks' next move. They should give further clues on how quickly the Fed is likely to scale back its huge stimulus programme in the coming months.
European shares edged higher as China's data was offset by positive euro zone data, including some showing gradual recoveries in Italy and Spain.
The pan-regional FTSEurofirst 300 was up 0.1 percent.
The euro rebounded as the euro zone data suggested the European Central Bank will not loosen its policy further any time soon.
The euro recovered from a one-month low during Asian trading to gain 0.1 percent at $1.3604, finding support as euro zone sentiment hit its highest in nearly three years.
In the U.S. bond market, benchmark 10-year Treasury notes were up 8/32 in price to yield 2.965 percent, down 3 basis points from late on Friday.
There was plenty of evidence to support the caution China data has fostered among investors.
Figures on Monday showing China's huge services sector slowed sharply in December to its lowest point since August 2011 came hot on the heels of a similar official survey on Friday and two other PMIs last week showing factory activity also soured.
GOLD, OIL RISE
Gold was the main beneficiary of the Asian tensions as it continued to rebound from last year's worst run in over three decades.
Spot gold rose to a near three-week peak of $1,245.86 an ounce in earlier trade and was last up 0.4 at $1,240.90 an ounce.
Oil bounced also after four days of falls. Brent crude oil rose above $107 a barrel, rebounding after its biggest weekly fall in six months on news of the restart of a key Libyan oilfield.
U.S. crude gained 5 cents to $94.01 a barrel in early trade. The contract lost $1.48 a barrel on Friday and posted its biggest weekly drop since June 2012.