WRAPUP 1-Euro zone downturn eases, US service sector accelerates

* Eurozone Composite PMI rises to 46.5 in November - Markit

* U.S. service sector growth accelerates - ISM

LONDON/WASHINGTON, Dec 5 (Reuters) - The euro zone's economic downturn appeared to ease slightly in November and the pace of growth in the U.S. service sector increased, suggesting some lifting of the chill that has gripped the global economy.

Survey compiler Markit said on Wednesday its Eurozone Composite PMI, which gauges business activity across thousands of companies in the 17-nation currency bloc, rose in November to 46.5 from 45.7 in October.

That marks a big improvement from a preliminary reading released 10 days ago, but there are few signs the region will emerge from recession any time soon.

The Markit euro zone composite PMI has lingered below the 50 mark that divides growth and contraction for all but one of the last 15 months.

France, Spain and Italy were the biggest drags on the euro zone economy through last month. Germany performed better.

Markit said the reading still pointed to a deepening of the euro zone's recession during the last three months of this year.

Many economists expect the recession, which began in the second quarter, to stretch into early next year.

"We see no signs of improvement that suggest that the (euro zone) economy might recover any time soon. Further contraction in GDP remains our baseline scenario at least until Q1 2013," said Annalisa Piazza, economist at Newedge Strategy in London.

The euro closed at a seven-week high on Tuesday and European shares continued their recent rally, although that was mainly due to comments from China's new leader which boosted expectations for global growth.

U.S. SERVICES INDEX IMPROVES

But on Wedneday, European shares lost momentum and the euro slipped as a disappointing Spanish bond sale and mixed economic data took the gloss off hopes for accelerating economic growth in China.

Europe's recession has dragged on the global economy, hitting exporters from Shanghai to Los Angeles.

Growth in China's services sector slowed in November as lacklustre growth in new orders and a surge of recent hires reduced work backlogs.

The HSBC Purchasing Managers Index for China's services sector released showed the index slipped to 52.1 in November from October's 53.5, as sales prices continued to fall despite a rise in input prices.

The U.S. economy, while being a relative bright spot on the global stage, has also struggled with flagging business confidence due to the risk of a renewed recession next year.

U.S. factory output has looked shaky in recent months due to weaker export demand and a softening of business investment plans.

This month, the pace of growth in the U.S. services sector increased slightly as a rise in new orders and business activity helped offset a fall in employment and prices.

The Institute for Supply Management said its services index rose to 54.7 last month from 54.2 the month before. The ISM reading topped economists' forecasts for growth of 53.5, according to a Reuters survey.

"The much larger service side of the U.S. economy remains relatively healthy," said Joseph Trevisani, a market strategist at Worldwide Markets in Woodcliff Lake, New Jersey. "It has so far avoided the contraction in manufacturing."

The ISM's factory activity index on Monday showed an unexpected contraction in November. The index also pointed to contraction during the summer of this year, but in November was at its weakest since 2009.