* Dollar strengthens on strong U.S. services, factory figures
* European shares rise after encouraging earnings reports
* Wall Street pares declines after data
* Asia hit by unexpected weakness in China services PMI (Adds close of European markets, quote)
New York, Aug 5 (Reuters) - The U.S. dollar strengthened and bond yields rose on Tuesday after strong data on factory orders and service-sector growth, while European shares posted a modest gain to stem a recent declines.
But stocks on Wall Street were modestly weaker, although the S&P 500 managed to hold above the 1,920 support level after pulling back from recent highs last week, its largest weekly drop in two years.
U.S. stocks started the session on a down note after weak figures out of China, where the HSBC/Markit services PMI fell in July to its lowest since November 2005, suggesting a recovery in the world's second-largest economy may need further government support.
But the dollar hit its highest level since September 2013 against a basket of currencies after the Institute for Supply Management said service-sector growth in the United States hit an eight-and-a-half-year peak on strong growth in new orders and employment.
Factory orders were also strong in July and data showed positive revisions to durable goods orders, a sign that the economy continues to improve. The euro fell to a day's low of $1.3357 after the U.S. data, while the dollar hit a high of 102.92 against the yen, continuing a trend of strength in the U.S. currency.
"The big picture is we are still kind of hung over on the good economic news from last week. That should propel markets forward, but there will be volatility and noise in the interim," said James Liu, global market strategist at JPMorgan Funds in Chicago.
"There is almost a sense of a gap between the economic numbers right now and how the market has performed over the past week."
U.S. 10-year Treasury yields hit a session high of 2.53 percent after the manufacturing and services data. The benchmark 10-year note was down 3/32, to yield 2.50 percent.
The Dow Jones industrial average fell 67.14 points, or 0.41 percent, at 16,502.14. The Standard & Poor's 500 Index was down 8.89 points, or 0.46 percent, at 1,930.10. The Nasdaq Composite Index was down 13.51 points, or 0.31 percent, at 4,370.38.
The MSCI All-World Index fell 0.5 percent.
European PMI figures showed the continent's economy was growing, as expected. But manufacturing remained weak and kept intact expectations the European Central Bank will ease monetary policy further, pressuring the euro.
Investors in Europe were cheered by forecast-beating results from German luxury carmaker BMW and France's third-biggest listed bank, Credit Agricole, among others.
The pan-European FTSEurofirst 300 index of leading shares gained 0.3 percent, a small recovery from its nearly 4 percent fall over the past two weeks on concerns over financial uncertainty about Portugal's Banco Espirito Santo, which was later bailed out.
In commodities markets, Brent crude slipped below $105 a barrel, falling 96 cents to $104.45 as ample supplies outweighed Middle East turmoil, while U.S. crude shed $1.08 to $97.21. (Reporting by Chuck Mikolajczak; Additional reporting by Daniel Bases; Editing by Dan Grebler)