* Eurozone Composite PMI rises to 46.5 in November -Markit
* U.S. service sector growth accelerates -ISM
* Global economic activity at eight-month high -JPMorgan
By Andy Bruce and Jason Lange
LONDON/WASHINGTON, Dec 5 (Reuters) - The euro zone's economic downturn appeared to ease slightly in November, while U.S. and worldwide data provided indications that the chill that has gripped the global economy is improving.
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 last month to a reading of 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. A reading below 50 indicates contraction.
Europe's recession, which began in the second quarter, has dragged on the world's economic output, hitting exporters from Shanghai to Los Angeles.
Wednesday's data, however, gave some hopeful signs for the broader global economy.
"Although global GDP growth remains muted, the latest PMI data are at least showing positive signs in the service sector," said David Hensley, economist at JPMorgan.
JPMorgan said its All-Industry Output Index, a gauge of activity across the world in private factories and services, hit an eight-month high in November of 53.7, rising from 51.0 in October.
Europe's struggle with its sovereign debt crisis has led to a credit crunch in the region, and economic output contracted in the second and third quarters.
In November, the biggest drags on regional economic activity came from France, Spain and Italy, Markit said. Germany performed better.
Markit said the readings still pointed to a deepening of the euro zone's recession during the last three months of this year. Many economists expect the recession to stretch into early 2013.
"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.
Growth in China's services sector slowed in November as lackluster 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 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.
In November, 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 in October. 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 factory index on Monday showed an unexpected drop in activity in November. The index also pointed to contraction during the summer of this year, but in November was at its weakest since 2009.