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* Euro lifted by above-forecast euro zone services data
* European shares rebound from Monday's sharp sell-off
* Brent crude close to $116 a barrel, gold flat
By Richard Hubbard
LONDON, Feb 5 (Reuters) - European shares, oil and the euro bounced back on Tuesday from a selloff caused by rising political risks in southern Europe, as data confirmed the region's economy is showing signs of recovery.
The euro, which had taken the brunt of the selling and fallen from a high of over $1.37 at the end of last week to under $1.35 on Monday, rose 0.3 percent to trade at $1.3560.
European shares followed a similar path, recovering from the Monday sell off, while U.S. stock index futures indicated Wall Street would rebound from its worst daily session since November when trading resumed later on Tuesday.
Analysts saw the market's gyrations as a necessary stage in a rally linked to signs of increasing euro zone economic stability and an improving global outlook, underpinned by the easier monetary policies of major central banks.
"Our working hypothesis remains that, after the correction, the trends in place before will continue, as the two main drivers are still there - namely central banks continuing to inject liquidity and more and more proof of an economic recovery," said Philippe Gijsels, head of research at BNP Paribas Fortis Global Markets in Brussels.
The markets regained their composure on Tuesday after data confirmed the euro zone's still struggling economy was starting to turn around.
Markit's Eurozone Composite PMI, which gauges business activity across thousands of companies and is seen as good gauge of future growth, rose in January to a 10-month high of 48.6 - though this still means the region's economy is contracting.
"The euro zone is showing clear signs of healing, with the downturn easing sharply in January and the region moving closer to stabilisation in the first quarter," said Chris Williamson, chief economist at Markit.
But the data also highlighted a growing divergence in the euro zone between the performance of its biggest economy, Germany, and those of other partners, leaving some doubts about the region's prospects.
Markit's composite German PMI chalked up its biggest one-month rise since August 2009, reaching its highest since June 2011. But in neighbouring France it fell to its lowest level in nearly four years.
"The downturn we saw at the end of last year is starting to peter out, but I don't think we're going to see any spectacular growth yet," said Peter Westaway, chief European economist at Vanguard Asset Management.
After the data, the broad FTSE Eurofirst 300 index of top European shares was up 0.6 percent while London's FTSE 100, Paris's CAC-40 and Frankfurt's DAX were between 0.3 and one percent higher.
Analysts said the euro and equity markets could see further volatility on Thursday when the European Central Bank holds its monthly policy meeting and President Mario Draghi is due to address a news conference.
None of the 75 economists surveyed in a Reuters poll last week expect the ECB to cut rates from their record low of 0.75 percent at Thursday's policy meeting, but Draghi may be pressed to comment on the recent sharp rise in the euro.
MSCI's world equity index was down around 0.1 percent reflecting an earlier sell-off across Asia when investors joined in the global correction in prices and ignored positive economic news from China.
The HSBC China services purchasing managers' index rose to a four-month high of 54 in January, underlining the strengthening momentum in the world's second-biggest economy, which is expected to grow 8.1 percent this year.
The MSCI index of Asia-Pacific shares outside Japan was down 0.9 percent, led by a steep 1.7 percent fall in Hong Kong shares, after the pan-Asian index had climbed to an 18-month high on Monday.
Investors will next look at data from the vast U.S. services sector, due later on Tuesday, to gauge the monetary policy outlook after recent releases have painted a mostly upbeat picture of the world's largest economy.
Bond markets were also stabilising on Tuesday after the sudden upsurge in political worries about Spain and Italy had caused a sharp rise in yields on peripheral euro zone debt and fresh demand for safe-haven German government bonds.
Spanish 10-year government bond yields eased back six basis points to 5.38 percent, while equivalent Italian yields were a four ticks lower at 4.43 percent.
German Bunds meanwhile rose slightly to be up four basis points at 1.67 percent.
Commodity markets were more mixed. Brent crude oil, which has dropped almost 1.5 percent since the start of the month, rose over $1 a barrel to $116.75 while growth-attuned copper slipped 0.2 percent to 8,290 a tonne.
Platinum and palladium consolidated around multi-month highs, as traders chose to sell into the rally to lock in profits, while gold was again little changed.
Palladium dropped 0.3 percent to $753.54 an ounce, having peaked at a 17-month high of $759.75 an ounce on Monday. Platinum was up 0.2 percent at $1,695.99 an ounce, off a four-month high of $1,705.25 hit in the previous session.
Gold, which has been trapped in a tight $1,660 to $1,680 range since late last week, again saw little movement with investors increasingly wondering whether its 12-year rally is now over.
Monetary stimulus was a driver of gold's rise in the last few years, and an improving U.S. economy has stirred thoughts that the Federal Reserve might curtail the bond-buying that has dominated its support efforts.
"People are mostly waiting for more data from the United States to assess how the economy is and whether quantitative easing will continue," said Ronald Leung, a dealer at Lee Cheong Gold Dealers in Hong Kong.