The European Commission will present the ministers with a proposal on a stabilization mechanism intended to provide a multi-billion euro safety net for other euro zone countries with bloated public finances such as Portugal, Spain or Ireland.
Bond yields of these countries have been rising sharply - increasing the risk premium investors carry to hold their debt - on market concern they may be next to need assistance.
The threat that markets would turn against the three states next triggered a call from euro zone leaders on Friday to come up with a solution to the crisis before markets open on Monday.
"We now see ... wolfpack behaviors, and if we will not stop these packs, even if it is self-inflicted weakness, they will tear the weaker countries apart," Swedish Finance Minister Anders Borg told reporters on arrival for the meeting.
"So it's very, very important that we now make progress, both when it comes to consolidation - not only long-term but short-term consolidation - but also when it comes to a common facility to deal with the urgent problems," he said.
Greece, which had a budget deficit of 13.6-14.1 percent of GDP in 2009 and debt of more than 115 percent of GDP, has already secured a 110 billion euro ($148 billion) three-year loan package from the euro zone and the International Monetary Fund after its costs of borrowing rose to unsustainable levels.
"We ... need resources to stop the market turmoil. If this goes on for more than a couple of days it will be very, very problematic for the recovery," Borg said.
EU sources said the European Commission will ask EU finance ministers to extend an existing aid mechanism for non-euro zone countries to nations in the single-currency bloc.
The commission will also ask the extraordinary meeting of ministers to raise the existing amount available under the mechanism, called the balance-of-payments facility, by 60 billion euros ($80.5 billion).
The maximum available now is 50 billion euros.
EU sources said the 60 billion top-up would be used as base capital, or collateral, for borrowing on the markets, which would allow the commission to raise up to 10 times that amount.
The 60 billion top-up would be guaranteed by all 27 members of the European Union and the loans, if paid out to an EU member, would carry conditions set by the International Monetary Fund, one EU source said.
Funds previously raised via the facility are rated AAA - top investment grade - by major credit ratings agencies.
As an additional measure for euro zone countries only, the commission will propose a separate mechanism of intergovernmental loans, the source said.
"We are going to defend the euro," Spanish Economy Minister Elena Salgado told reporters as she arrived for the talks.
A similar mechanism has already been successfully used in the cases of Latvia, Romania and Hungary after the pool of money available was increased to 50 billion euros last year.
The mechanism could be used on the basis of an EU law which says that if a member of the 27-nation bloc is in difficulties caused by circumstances beyond its control, EU ministers may, under certain conditions, grant it financial assistance.
"The situation in the financial markets has gone in a very bad direction, even though the Greek situation was brought under control," Finnish Finance Minister Jyrki Katainen told a news conference in Helsinki.
"Now we have to do everything we can to bring stability in time," he said.
The ministers' meeting follows a summit of euro zone leaders on Friday, which asked for a European Stabilization mechanism to be ready before markets open on Monday.
Some economists said the move was welcome news, but it would cure the symptoms, rather than the disease.
"By putting in place additional safeguards for the euro area financial system, governments finally appear to be rising to the challenge of the sovereign debt crisis," Morgan Stanley said in a research note to clients.
"But, like the measures taken before - for the benefit of Greece - a stabilization fund is just buying time for distressed borrowers," the bank said.
It added: "The fiscal policy action taken in these countries during this "extra time" is essential. If yet another rescue mechanism isn't followed by aggressive austerity measures, the problem just continues to fester - and could eventually spread even wider." Euro zone leaders vowed on Friday to accelerate their fiscal consolidation programs to make sure they meet targets set by EU finance ministers this year and in the coming years.