* Wall Street opens slightly lower
* Dollar cuts early declines after U.S. data
* U.S. and euro zone service sector growth picks up
By Leah Schnurr
NEW YORK, Aug 5 (Reuters) - Stocks on Wall Street pulled back from record levels on Monday, while better-than-expected growth in the U.S. service sector helped the dollar cut its losses.
Growth in the euro zone's service sector picked up slightly, while the U.S. sector accelerated more strongly in July, keeping declines in U.S. and European equities in check.
The S&P 500 has risen for five of the past six weeks, gaining more than 7 percent over the period. The index closed at an all-time high on Friday despite a disappointing read on the U.S. labor market.
Given that advance, further gains may be difficult at these levels, analysts said, especially with the corporate earnings season largely over.
"Growth continues to be anemic, even as we're at record levels in the market, suggesting we're overbought on some levels," said Mark Martiak, senior wealth strategist at Premier/First Allied Securities in New York.
The Dow Jones industrial average was down 37.65 points, or 0.24 percent, at 15,620.71. The Standard & Poor's 500 Index was down 1.25 points, or 0.07 percent, at 1,708.42. The Nasdaq Composite Index was up 2.64 points, or 0.07 percent, at 3,692.22.
European shares traded flat around a two-month high, while the MSCI world equity index slipped 0.15 percent.
Some investors took Friday's weaker-than-expected U.S. jobs report as an indication that the Fed was likely to hold steady with its monetary stimulus program. Less stimulus will eventually lead to a rise in interest rates, making the dollar more attractive for investors.
The U.S currency fell 0.3 percent to 98.67 yen, but was up 0.1 percent against a basket of currencies following the service sector report.
The central bank is currently buying $85 billion in bonds to keep borrowing costs low, a program that has helped U.S. stocks surge nearly 20 percent this year.
The outlook for the global economy improved slightly with purchasing managers' surveys covering thousands of companies worldwide. One such report showed China recovered some momentum in July, while activity in the euro zone expanded for the first time in 18 months.
It is still unclear if the recession-hit euro area has turned the corner, but the data pointed to more sustainable strength in Britain, where the services sector is growing at its fastest pace in more than six years.
Growth in the U.S. service sector also accelerated, picking up from a three-year low as new orders surged to their highest level in five months.
That report weighed on U.S. debt prices, with 10-year Treasury notes trading 14/32 lower in price, yielding 2.6515 percent.
For commodity markets, the latest growth data was seen as not strong enough to lift demand, especially from leading oil and metals consumer China.
Brent crude initially rose above $109 a barrel as supply disruptions by Middle East and North Africa producers lifted prices, but it later slipped 62 cents to $108.33.
U.S. crude gave up 33 cents to $106.61.