* Euro dips towards $1.29, falls 0.9 pct vs yen
* Europe sets Monday deadline for Cyprus bailout deal
* European shares down 0.5 pct after weak PMI data
* Asian shares lifted by rise in China factory activity
By Richard Hubbard
LONDON, March 21 (Reuters) - Signs the euro zone's economic downturn is deepening and worries over a possible financial meltdown in Cyprus sent world shares, oil and the single currency lower on Thursday.
The falls could have been greater but for earlier data showing a pick-up in Chinese factory activity and the commitment by U.S. Federal Reserve on Tuesday to stick with its ultra-loose monetary policy stance.
Wall Street shares reflected the precarious balance of risks indicating a flat performance when trading starts.
But the euro and European shares moved decisively lower, with the single currency briefly dipping below $1.29 to the dollar, following weak readings of the March Purchasing Manager's Indexes (PMIs), which showed activity across the 17-nation currency bloc slowing from already weak levels.
The data revealed that German growth was starting to suffer from the euro zone's renewed problems and again highlighted a widening chasm with France, the region's second largest economy.
"It (PMI data) does not look good," Antonio Garcia Pascual, chief southern European economist at Barclays. "Maybe we were expecting it in France but the weakness in Germany was a surprise."
The FTSEurofirst 300 index of top European shares extended its falls after the data to be down 0.5 percent to 1,192.21 points. The main market indexes in London, Paris and Frankfurt were all around 1.0 percent lower.
Yields on German 10-year government bonds, used as a safe-haven in times of market stress, stayed close to their 2013 lows at 1.38 percent, barely changed on the day.
MSCI's world equity index dipped only about 0.1 percent, but remains on course for its worst week since November last year when worries about the U.S. fiscal cliff were driving markets lower.
Apart from the bleak economic numbers, market attention was firmly on Cyprus, where crisis talks among political leaders resumed to seek a new bailout plan which could involve Russia.
The European Central Bank has set a Monday deadline for Cyprus to agree a new plan, threatening to cut off funding to the island's cash-strapped banks if a programme is not agreed by then with the European Union and the IMF.
Cyprus has faced the prospect of bankruptcy since Tuesday when its tiny parliament voted unanimously against a levy on bank deposits to raise 5.8 billion euros ($7.5 billion) demanded by the EU under a 10 billion euro rescue deal.
The worries about Cyprus look to be contained for the moment with Spain able to sell 4.5 billion euros of new bonds on |Thursday in an auction that saw strong demand and resulted in lower yields than at recent debt sales.
"All in all, no signs of Cyprus contagion in this sale," said Marc Ostwald, a strategist at London-based Monument Securities.
Spain's 10-year bond yield in the secondary market fell 10 basis points on the day to 4.9 percent.
Most markets had begun the day firmly underpinned by the Federal Reserve's latest policy statement at which the current aggressive policy stimulus programme was left unchanged despite recent improvements in the U.S. economy.
Fed Chairman Ben Bernanke said the central bank might slow the pace of its bond buying but only after the labour market showed sustained improvement over a number of months.
Asian shares gained a further lift when the HSBC Purchasing Managers' Index for China showed a rise to 51.7 in March from 50.4 in February, pointing towards solid but not spectacular first-quarter growth in the world's second-largest economy.
The MSCI's broadest index of Asia-Pacific shares outside Japan, rose 0.1 percent after that data.
Japan's Nikkei stock average climbed 1.3 percent, hitting a 4-1/2-year high as exporters gained on the Fed's commitment but also expectations of further monetary easing by the Bank of Japan.
The BoJ's new governor, Haruhiko Kuroda, in his first news conference, reaffirmed the commitment to expand Japan monetary stimulus to beat deflation, sending 10-year government bond yields to a near-decade low on Thursday.
Oil markets drew support from the Chinese data to hold on to much of their previous day's gains but have eased slightly due the concerns about Cyprus and the wider euro zone.
U.S. crude futures fell 42 cents to $93.08 a barrel while Brent eased 44 cents to $108.28.
The pledge by the Fed a pledge to keep spending $85 billion a month buying bonds lent support to gold. Spot gold firmed 0.2 percent to $1,608.56 an ounce, though off a three-week high of $1,615.16 hit earlier this week.