The benchmark Europe Stoxx 600 share index finished the day by climbing 2.5 per cent to 229.08 points.
At one point during the day, the Stoxx 600 index had jumped 2.7 per cent before it slumped 2.1 per cent. The index has is down about 10 per cent on the week.
European markets also took their lead from a more positive mood prevailing on Wall Street following better-than-forecast weekly job claims.
New York's Dow Jones Industrial Average was trading up by 2.3 per cent at 10,977 points as European share markets closed.
Fears about the world economic outlook and the risk that the eurozone debt crisis could engulf other members of the 17-state currency bloc - notably France - resulted in shares see-sawing around the world throughout the day.
In particular, French banking stocks were again in the spotlight as a result of concerns about their investment in bonds in vulnerable members of the eurozone such as Italy, Spain and Greece. Paris's main CAC 40 index closed up 2.89 per cent.
Meanwhile, Frankfurt's DAX ended 11 days of straight losses to close Thursday up by 3.3 per cent. Shares in London finished the day up 3.11 per cent.
The focus on France followed the weekend downgrade of the US's triple-A credit rating which has resulted in markets focusing on the 15 nations enjoying a top debt rating. This includes Switzerland, Britain, Singapore and Australia.
Markets have been concerned whether France will be able to retain its triple-A rating in the light of the nation's high debt-and-deficit levels.
With a debt ratio of 82 per cent of gross national product (GDP) and a deficit of 7 per cent of GDP, France's two key fiscal barometers stand well above the budget targets for eurozone member states.
In addition, economic growth data to be released Friday is forecast to show France's economy expanded by just 0.3 per cent during the second quarter.
German Chancellor Angela Merkel and French President Nicolas Sarkozy are due to meet next week in Paris to discuss the euro debt crisis, her office announced Thursday.
"Nobody knows now what is the solution to the problems. There are many, even quite promising approaches but not a fundamental solution," said Joerg de Vries-Hippen, who heads up European equities for RCM/Allianz Global Investors.
With a limited amount of economic data expected by the end of the week, analysts have been warning that markets risked been easily spooked by speculation as they try to seek guidance.
In the meantime, with investors still reeling from the chaos on share markets over the past week the current corporate reporting season, which has been underway on both sides of the Atlantic, has being pushed to one side.
While company results in the US have been relatively encouraging, corporate results in Europe have been more mixed.
The rise in shares helped to undercut the gold price, which fell back more than 2 per cent in late European trading after hitting an all-time high of 1,800 dollars an ounce in the last 24 hours.
At the same time, oil climbed by 0.5 per cent to over 83.32 dollars a barrel in late trading.
The pickup in European and US stocks came after Asian bourses ended the day by clawing back losses recorded in the day to chalk up moderate falls.
The MSCI Asia Pacific Index fell 2.4 per cent during the day, but recovered most of the drop, and was down 0.3 per cent at close of trading.
The Shanghai composite index, however, bucked the trend gaining 1.27 per cent as the trading day came to an end.
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