Among other tools, the ministers said following their 8-hour session in Brussels, they will consider using the bailout fund, called the European financial stability facility, to buy bonds from struggling countries on the open market, Financial Times reported.
"There are a variety of ways of enhancing the flexibility of the EFSF," Olli Rehn, the European Commission's economic chief, said.
The Times said the ministers also agreed to lower interest rates for countries now receiving bailout loans from the EU.
Financial Times noted the idea of using the bailout fund had been blocked earlier this year by Germany and the Netherlands, which at the time were loath to commit taxpayer money to the problem. However, Monday both countries agreed to reconsider the issue, though a specific structure was not outlined.
"We stressed the need to make Greek debt more sustainable," the Times quoted Jean-Claude Juncker, the Luxembourg prime minister and euro group president, as saying.
He said a proposal to do just that would be presented "as soon as possible."
While Greece is the most pressing situation, a default by Italy was the latest fear as European policymakers huddled in Brussels, officials said.
A Friday panic wave of selling hit Italian bank stocks at Milan's Borsa Italiana, Italy's main stock exchange.
Milan's main stock index, the FTSE MIB, closed down 3.5 percent -- Italy's biggest bank, UniCredit SpA, fell almost 8 percent -- and the spread between 10-year Italian and benchmark German bond yields reached a record 2.47 percentage points, pushing up Italy's borrowing costs to a record 5.27 percent.
Italy has a debt equal to 120 percent of annual gross domestic product, one of the eurozone's highest.
The Italian Securities and Exchange Commission late Sunday introduced immediate measures to curb speculative attacks, requiring market operators to disclose short-selling moves above certain levels.
The measures will remain in effect until Sept. 9, the commission said.
The run on bank stocks came amid fears Italian Prime Minister Silvio Berlusconi may fire Finance Minister Giulio Tremonti, who has been praised for his handling of the economy during the financial crisis and for maintaining control of the budget deficit.
Berlusconi told the Italian newspaper la Repubblica Friday Tremonti was "the only minister who is not a team player."
Tremonti has been resisted the tax cuts Berlusconi and other politicians desire, The New York Times reported.
Greece, Ireland and Portugal have been bailout recipients. But economists say a bailout of Italy would dwarf all that has gone before.
"The [bailout] fund can't cope with Spain, let alone Italy -- and each country getting into trouble means that one less country is contributing," an analyst told The Daily Telegraph of London.
EU officials have so far been treating the debt crisis as a liquidity issue that can be dealt with using bailouts, analysts said.
But if economies the size of Italy's get caught up in it, broader structural changes throughout the eurozone will likely have to be made, they said.
Notable deaths of 2014 [PHOTOS]