The European Union's (EU) economic affairs commissioner has said Europe must "resist alarmism" amid the latest fears over the Irish Republic's debts.
Olli Rehn said he was "concerned" about public debate on the eurozone.
Late on Tuesday a meeting of eurozone ministers meeting in Brussels broke up with no concrete plan of action.
But speaking after the talks finished, Mr Rehn said the EU would, however, step up work on support for Ireland "with an accent" on its banks.
Earlier, the Irish Prime Minister, Brian Cowen, reiterated that the Republic of Ireland had not asked for bail-out money and that the Irish economy was well funded until next year.
He said his country was working with European partners to deal with the debt issue, but that his country was neither "immune or unique" amid the recent economic crisis.
The Irish government, the European Commission, the European Central Bank and the IMF have also met to discuss the country's "serious banking problems".
Mr Cowen tried to play down the growing sense of crisis across the eurozone, telling the Irish parliament that these were just a continuation of ongoing discussions it had been having with European institutions for some time.
Earlier, the EU Council president, Herman Van Rompuy, warned that the European Union was in a "survival crisis" over eurozone debt problems, as the economic health of members such as the Republic of Ireland and Portugal came under fresh scrutiny.
Mr Van Rompuy said that if the euro failed, so too would the EU.
However, he added he was "very confident" the problems could be overcome.
Uncertainty has caused the cost of Irish, Portuguese and Spanish government borrowing to rise significantly over recent weeks.
Rising yields are not an immediate concern for the Irish Republic, as it does not need to borrow money on the markets this year.
But it is for countries such as Spain, which held an auction of government bonds earlier, and other countries facing large deficits.
The Spanish treasury secretary called on the Republic to act quickly to end market uncertainties.
Portugal's finance minister Fernando Teixeira dos Santos has urged Dublin to do the right thing for the euro and accept a bail-out.
The BBC's business editor Robert Peston said that much hinged on the stance of the European Central Bank (ECB) - which has propped up the Irish Republic's banking system with loans it could not get on the money markets.
"Without the financial support of the ECB, Ireland would be bust right now," he said.
"But if there is the faintest sign that the ECB wants to withdraw the succour it has provided to weak eurozone banks, Ireland will no longer have a choice, it will have to go cap in hand either to its EU partners or to the IMF."
The Irish Republic's Europe Minister, Dick Roche, admitted that there were major liquidity problems at the country's banks.
However, he said that his government had made major spending cuts which would be continued in its upcoming budget, and added that he hoped there would be "solidarity" from European colleagues at the Brussels meeting.
"I would hope after the meeting there would be more logic introduced into this," he told the BBC.
"There is no reason why we should trigger an IMF or an EU-type bail-out. There is a problem with liquidity in banks, there is no doubt about that. But I don't think that the appropriate response to that would be for the European finance ministers to panic."
There are a range of funds which troubled nations could access - including the European Financial stability facility - 440bn-euro (£372bn) pot of money set up to aid eurozone countries that run into debt difficulties.
And while the UK is not part of the eurozone, its taxpayers could end up footing some of the bill for any bail-outs.
For example, there is the European Financial Stability Mechanism - a 60bn-euro, EU-wide scheme, which countries can draw on and to which the UK contributes 12%.
Also, if the International Monetary Fund (IMF) is asked to step in, the UK would fund 4.5% of any aid.
Budget brought forward?
Irish banks have struggled since 2008, when the Republic suffered a dramatic collapse of its property market.
House values have fallen between 50% and 60% and bad debts - mainly in the form of loans to developers - have built up in the country's main banks, bringing them to the verge of collapse.
Reports suggest the Republic will try to reassure markets by bringing forward details of its four-year financial plan to next week.
The proposals will be severe. It has said it will impose unprecedented spending cuts or tax rises totalling 6bn euros (£5bn) to try to bring its underlying budget deficit down from about 12% to between 9.5 and 9.75% next year.
While intended to boost confidence in the country's finances, investors fear the budget cuts could plunge the Republic back into recession, leading to further losses to the government via falling tax revenues and higher benefit payments.