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The outline of a large and ambitious eurozone rescue plan is taking shape, reports from the International Monetary Fund (IMF) in Washington suggest.
It is expected to involve a 50% write-down of Greece's massive government debt, the BBC's business editor Robert Peston says.
The plan also envisages an increase in the size of the eurozone bailout fund to 2 trillion euros (£1.7tn; $2.7tn).
European governments hope to have measures agreed in five to six weeks.
Turning the present outline into a practical reality will be immensely difficult, our editor says.
But he adds that the price of failure could be a financial crisis that would probably turn anaemic growth into a recession or worse.
Investors have so far been unimpressed with the speed at which policymakers have dealt with the eurozone debt crisis, and analysts say that action, not words, are needed to calm volatile stock markets.
Over the weekend, the G20 reasserted its commitment to "a strong and co-ordinated international response" to the crisis, but analysts warned this would not be enough to satisfy investors.
"Given that there were no details on how [the G20 would combat the crisis], it will not do much to alleviate market stress without some concrete action," said Mitul Kotecha at Credit Agricole.
European markets fell at the start of trade on Monday but then rallied. By lunchtime, Germany's Dax index and France's Cac 40 were both up more than 3%.
Earlier, Asian markets had fallen, with Japan's Nikkei index closing down 2.2%, Hong Kong's Hang Seng falling 1.5% and South Korea's Kospi dropping 2.6%.