Global stocks rallied for a second day with a strong advance in Europe and Asia on Tuesday on signs that EU and world leaders are preparing a blockbuster response to the eurozone debt crisis.

The euro steadied against the dollar as Greek Prime Minister George Papandreou headed for talks with German Chancellor Angela Merkel on containing the crisis which US President Barack Obama said was scaring the world.

"There has been no concrete alteration in the structure of the eurozone since the end of last week but the market has been willing to clutch at the idea that politicians at least recognise there is an urgent requirement for action," said Rabobank analyst Jane Foley.

The euro dipped to $1.3515 from $1.3523 late in New York on Monday.

In early European deals, London's FTSE 100 index of leading shares rallied 2.27 percent to 5,204.11 points, Frankfurt's DAX 30 surged 3.58 percent to 5,536.67 points and in Paris the CAC 40 jumped 3.09 percent to 2,947.76.

Other markets posted similar strong gains, with Madrid and Milan both up more than 2.0 percent.

Banking shares led the charge higher, with BNP Paribas rocketing nearly 9.0 percent and Societe Generale up 7.4 percent in Paris on rumours of a recapitalisation plan for French lenders exposed to the Greek debt crisis.

European stock markets had already risen strongly on Monday. Asian equities rebounded on Tuesday on bargain-buying after recent heavy selling caused by the eurozone crisis, but traders remained cautious because of mixed messages from EU leaders, analysts said.

The region's gains followed a rally on Wall Street overnight after reports filtered through that a plan was emerging to stop the debt crisis.

Tokyo closed up 2.82 percent, Hong Kong rocketed 4.15 percent and Sydney advanced 3.64 percent.

Investors moved in to buy cheap shares on Tuesday as a report emerged that European officials were working on a scheme to use funds for the eurozone bailout facility to shore up financially strapped European banks.

There was also talk that a 50-percent "orderly" haircut for Athens' creditors will now be required to make a difference.

Adding to that was speculation that France was drawing up plans to re-capitalise the country's ailing banks amid persistent worries over their exposure to Greece.

Foley said: "Further delays in a solution to the crisis are almost inevitable suggesting that the euro is far from out of the woods."

Analysts at Moneycorp in London referred to report and rumours that the EU EFSF support fund might be boosted to 3.0-4.0 trillion euros ($4.0-5.4 trillion).

They commented: "The latest plan is rumoured to involve allowing Greece to default, allowing it to stay in the eurozone, pumping billions into Europe's biggest banks and, of course, the extra firepower of the EFSF."

The falls on stock markets last week wiped trillions of dollars from the combined value of global stock markets.

"There is still plenty of risk out there that could trip up markets," said Kathleen Brooks, an analyst at trading group. "We can't forget that the US still has its own problems."

Europe's failure to tackle crippling Greek debt is "scaring the world," US President Barack Obama warned on Monday as Germany rejected plans to boost funding for the EU's debt rescue facility.

Europe "never fully dealt with all the challenges that their banking system faced," Obama said on Monday.

"It's now being compounded with what's happening in Greece," he said. "So they're going through a financial crisis that is scaring the world."