* Rise in China Jan PMI data shows economy may be bottoming
* Fitch cuts Russian sovereign debt rating
* Decline in euro zone service sector slows
* U.S. private sector job losses slow in January (For more on the global financial crisis, click on)
By Simon Rabinovitch and Mike Peacock
BEIJING/LONDON, Feb 4 (Reuters) - Improved manufacturing data from China on Wednesday suggested its downturn may be bottoming out and U.S. employment figures were not quite as bad as forecast, but crisis-hit Russia's sovereign debt rating was cut.
U.S. data showed another steep drop in private sector employment but the rate of job losses slowed in January for the first time since September last year. Hopes for a recovery in China helped to lift Asian share prices and a parallel report showed the pace of decline in Europe's dominant service sector also slowed.
But the Russian debt rating downgrade sent the euro tumbling against the dollar and the yen, due to fears of a steep economic downturn across much of central and eastern Europe.
The euro zone services Purchasing Managers' Index of around 2,000 companies covering banks to cafes rose to 42.2 in January from 42.1 in December. The downturn worsened in Germany and Spain but slowed markedly in France and Italy.
The financial crisis, stemming from a collapse in risky U.S. home loans which devastated the banking sector, has pushed the United States, euro zone, Britain and Japan into recession.
Russia has been as hard hit as most with foreign capital fleeing its shores. Ratings agency Fitch downgraded Russia's sovereign debt rating to 'BBB' and said further cuts were possible.
"The downgrade reflects the negative impact on Russia from the fall in commodity prices and the dislocation to global capital markets that has left Russian banks and companies struggling to refinance external debt," said Edward Parker, Head of Emerging Europe in Fitch's Sovereigns team.
The agency also said it was concerned by the depletion of Russia's reserves, which have shrunk by a third, or around $200 billion, since August as Moscow sought to control a slide in the rouble and compensate for record capital outflows.
The cut brought Fitch in line with rival Standard and Poor's, which cut Russia to two notches above a "junk" rating in December. But analysts were worried about the wider region.
"Increasing concerns over Russia and central Europe must be watched very closely. A slowdown in that region has negative implications for European banks," said Ian Stannard of BNP Paribas.
Some western European banks have lent heavily into the region and Russia had been a big buyer of euro zone exports when oil prices were high.
The dollar held its gains against the euro after the U.S. employment data. ADP Employer Services said private employers cut 522,000 jobs in January -- slightly fewer than forecast -- after a revised 659,000 jobs were lost in December.
This marked the first slowdown for four months but analysts were cautious before wider U.S. payrolls data on Friday. "I wouldn't put too much meaning into this report. Overall, aside from the the job losses, consumption all over the world is down. That's troubling," said Win Thin, senior currency strategist at Brown Brothers Harriman in New York.
GLIMMERS IN CHINA
Policymakers fear a new wave of protectionist policies could result from the global crisis and there are disturbing signs of social unrest and strikes across Europe
China, too, fears mass unrest if it cannot generate the eight percent economic growth rate reckoned to be necessary to create enough jobs for its workforce. An official said on Monday that about 20 million rural migrants had already lost their jobs.
But there are signs its economy may improve soon.
China's official purchasing managers' index for January rose to 45.3, up from 41.2 in December and a record low of 38.8 plumbed in November.
"China's GDP growth will be V-shaped in 2009, with the bottom already being reached in Q4 2008," said Mingchun Sun, an economist with Nomura in Hong Kong, in a note.
China unveiled a $585 billion spending plan in November and central bank governor Zhou Xiaochuan said in remarks published on Wednesday that the pump-priming was working.
"According to economic figures for December, the domestic stimulus policies have achieved initial results," Zhou told the Financial News, mouthpiece of the People's Bank of China.
EUROPE NEARING THE BOTTOM?
Data from the developed world has remained mostly gloomy -- Wednesday's figures showed euro zone retail sales fell more than expected year-on-year in December and November sales were revised, showing a much deeper drop than before.
But Europe's PMI figures offered a ray of hope. The survey's business expectations index climbed to 46.4 in January from December's near-record low of 42.3, a sign that the worst may be over.
"We are likely to see a significant contraction in GDP in Q1," said Nick Kounis, economist at Fortis. "Still, the pace of contraction should slow relative to Q4, which we think will prove to be the deepest point of the recession."
Britain's services sector also slid less sharply than expected last month. Its services PMI posted the highest reading since September, when Lehman Brothers collapsed.
Corporate evidence was less encouraging. Japan's Panasonic Corp, the world's No.1 plasma TV maker, warned it would post an annual loss of $4.2 billion and said it would cut about 15,000 jobs as it grapples with a stronger yen and slowing demand.
Earnings withered at Munich Re in the final three months of last year as the financial crisis intensified but the world's biggest reinsurer forecast improving prices in 2009.
Global economic woes are hurting even wealthy Norway. Its central bank cut its main interest rate by half a percentage point to 2.5 percent on Wednesday. (Addtional writing by David Stamp; Editing by Greg Mahlich)