Dealers said decisions by the European Central Bank and the Bank of England to keep interest rates on hold were as expected and their readiness to offer fresh stimulus measures was welcomed.
The BoE said it would pump another £75 billion ($115 billion, 87 billion euros) into the stalled British economy under its Quantitative Easing policy while the ECB will offer banks longer term concessional funding.
News overnight of the death of Apple founder Steve Jobs was a major talking point as tributes flooded in but analysts said his passing did not have a wider market impact, with the company's shares down sharply in early trade.
In London, the FTSE 100 index of top shares was up 1.73 per cent by mid-afternoon, with Frankfurt's DAX gaining 0.71 per cent and in Paris the CAC 40 rose 1.64 per cent.
In New York, the market opened slightly higher, picking up on the European and Asian leads, but then fell back as investors consolidated Wednesday's sharp gains.
The blue-chip Dow Jones Industrial Average was down 0.47 per cent at around 1345 GMT per cent, the broader S&P 500 was off 0.43 per cent while the tech-heavy Nasdaq Composite slipped 0.36 per cent.
Apple shares fell 0.36 per cent.
In foreign exchange deals, the European single currency eased to $1.3341 from $1.3388 in New York late Wednesday. The dollar fell to 76.65 yen from 76.82 yen.
Hopes for help for the banking system got another boost Thursday as European Commission president Jose Manuel Barroso said the EU executive was seeking "coordinated action" in all 27 European Union nations to recapitalise banks.
"We are now proposing to the member states to have a coordinated action to recapitalise banks and get rid of toxic assets they may have," Barroso said in a television interview.
The statement came after France and Belgium earlier this week agreed to bail out Dexia, the first European bank to be dragged down by the eurozone debt crisis and which also had to be rescued in the 2008 global financial crisis.
The debt crisis is now seen as threatening the banks exposed to distressed sovereign debt which now find it increasingly hard to secure short-term funding in the interbank money market.
"The markets are in recovery mode at the moment and seem to be wishing on a prayer that European leaders are going to find the answer in the coming weeks," said Simon Denham, head of Capital Spreads trading company.
"Today is all about central bank decisions," Denham said.
The BoE has kept interest rates at a record low 0.50 per cent since March 2009 when it began pumping £200 billion ($308 billion, 233 billion euros) into the economy.
Stocks in Europe had closed sharply higher on Wednesday, bouncing back from recent heavy losses on hopes that European nations would support their banks to prevent the eurozone debt crisis from spreading.
Asia's stock markets soared on Thursday, boosted by another strong performance on Wall Street and hopes European leaders will come together to plan a route out of the crisis.
Sentiment was also lifted by better-than-expected US economic data that eased concerns the United States is slipping into recession although all eyes now are on Friday's full government employment report.
Hong Kong soared 5.67 per cent, Tokyo jumped 1.66 per cent, Seoul rallied 2.63 per cent and Sydney gained 3.65 per cent. Shanghai was closed for a public holiday.
Markets have been hammered in recent weeks as Europe's leaders bicker over a plan to help Greece avoid a default and find a way out of its debt crisis, which many fear could plunge the global economy into another recession.
The International Monetary Fund on Wednesday urged Europe to balance growth with austerity and called for a "more than overdue" solution to the crisis, warning of recession next year if it fails.
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