Growth in the U.S. service sector eased last month, and new orders for factory goods fell in October, tempering recent optimism that the U.S. economy may be poised for a more vigorous rebound.

The Institute for Supply Management said on Monday its services index fell unexpectedly to 52.0 last month from 52.9 the month before, dragged lower by a decline in employment.

Although the headline number for the services index was at its weakest since January 2010, business activity and new orders both improved, showing the mixed nature of expansion that also was evident in the upbeat jobs report for November.

An ISM reading above 50 indicates expansion.

The economy has improved, (but) it is still not growing very quickly, said Cary Leahey, managing director at Decision Economics in New York.

This is the first disappointing indicator we've seen in the last couple of weeks.

Most economists continue to forecast that the United States will gradually expand at roughly a 2 percent rate next year, steering clear of recession as long as the euro-zone debt crisis is contained.

Following a series of positive readings for factory output and consumer spending, some economists think the U.S. economy will accelerate in the fourth quarter.

Macroeconomic Advisers, for example, raised its forecast for fourth quarter growth to a 3.0 percent annual rate, citing underlying strength in factory orders and shipments.

Pointing to growth in services, the ISM's gauge of new orders rose to 53.0 from 52.4.

It's not as if we went into negative territory. It's just not as strong as you would like to see, said Marc Pado, a U.S. market strategist at Cantor Fitzgerald & Co. in San Francisco.

U.S. stocks held onto gains following the ISM report as optimism grew that an upcoming Europeans Union summit would break new ground to resolve the euro zone debt crisis.

French President Nicolas Sarkozy said on Monday that France and Germany have agreed on a series of reforms to address the crisis. He was speaking after holding a meeting with German Chancellor Angela Merkel.

Resolving the euro zone's debt troubles would lift a dark cloud looming over the U.S. economy. Failure on the part of the Europeans, however, could still derail the U.S. recovery.

U.S. government debt prices fell, while the dollar weakened against the euro.

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Graphic: U.S. services sector:http://link.reuters.com/ham45s

Graphic: U.S. and world services PMI: http://link.reuters.com/gam45s

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FACTORY ORDERS FALL

The United States is still limping back from the punishing 2007-2009 recession, with economic growth hampered by a mountain of household debt and high unemployment.

After a dismal first half of the year marred by high gasoline prices and a Japanese earthquake disaster that stung global manufacturing, U.S. economic growth rebounded in the third quarter to a 2.0 percent annual rate.

That is weaker than in previous recoveries, although growth could pick up in the last three months of the year.

A report last week showed the U.S. jobless rate fell to 8.6 percent in November, although it remains well above its pre-recession trend.

In a separate report on Monday, new orders for U.S. factory goods fell in October for the second straight month, suggesting a possible softening in manufacturing. That area of the economy has been a key support for the recovery.

The Commerce Department said orders for manufactured goods decreased 0.4 percent.

Economists had forecast orders would fall 0.3 percent after a previously reported 0.3 percent increase in September.

(Writing and additional reporting by Jason Lange in Washington; Further reporting by Ellen Freilich and Chris Reese in New York; Editing by Neil Stempleman and Padraic Cassidy)

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