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The yields on Italian and Spanish bonds also continued to rise as worries over the two countries grew.
On Monday, eurozone finance ministers said they were ready to pass new measures to stop the crisis spreading.
The euro was also lower, falling to a four-month low against the dollar at $1.3835.
'Contagion risk' The concern is that Italy and Spain may have to follow Greece, Portugal and the Republic of Ireland and seek a European Union and International Monetary Fund (IMF) bail-out.
On Monday, eurozone finance ministers said increased efforts to "improve the euro area's systemic capacity to resist contagion risk" would include "enhancing the flexibility and the scope" of the European Financial Stability Facility (EFSF).
This is the bail-out fund to which eurozone member states contribute.
Finance ministers also agreed to look at lowering the interest rates that Greece, Portugal and the Irish Republic have to pay, plus lengthening the maturities of their loans.
"Ministers reaffirmed their
absolute commitment to safeguard financial stability in the euro area,"
the finance ministers said in a statement after eight hours of talks in
Brussels.
Italian cuts
Eurozone finance ministers have been meeting in Brussels on
Tuesday with their colleagues from European Union nations that do not
use the euro. Concern that Italy could be the next country to require a financial bail-out comes as Italy's Finance Minister, Giulio Tremonti, announced that he would leave Tuesday's talks early so he could continue to work on an austerity budget to reduce Italy's public deficit.
He has proposed 48bn euros ($67bn; £42bn) in budget cuts over three years and aims to cut the deficit to zero by 2014 from this year's 3.9% of gross domestic product.
Politicians are talking about panic in the markets and deliberate financial speculation.
But until they give a clear lead on how they intend to deal
with the next phase of eurozone debt problems, particularly in Greece,
then the sense of crisis will not dissipate.
The eurozone does now seem to be moving towards the idea that some form of default in Greece may be needed to help Athens cut its debts, as part of a second big financial bailout.
But the only promise is that decisions will be made shortly - and the lack of certainty continues to provoke anxiety.
The eurozone does now seem to be moving towards the idea that some form of default in Greece may be needed to help Athens cut its debts, as part of a second big financial bailout.
But the only promise is that decisions will be made shortly - and the lack of certainty continues to provoke anxiety.
However, financial markets were
unsettled by remarks from Prime Minister Silvio Berlusconi, who
indicated in a newspaper interview that the austerity plan might not
have full cabinet support.
Shares in Italian banks were down sharply in early trading, with Intesa SanPaolo losing 4% and UniCredit heading 7% lower.However, both then rebounded after the Italian government announced a successful sale of 12-month bonds, albeit at a high price.
Intesa and UniCredit were both up 2.3% on the day, while Italy's main share index, the FTSE MIB, reversed earlier losses.
Yet in a sign that investors remain more risk-averse to Italy, the yield on Italian 10-year bonds on Tuesday increased to 5.8% from 5.6% on Monday.
Meanwhile, yields on 10-year bonds issued by the Spanish government rose to 6.3%, from 6.1%.
Analysts say both these yields are now close to levels at which the two countries will have problems servicing their debts.
Asian shares had earlier closed lower, with the situation in the eurozone being closely monitored around the world.
Japan's Nikkei index lost 1.4%, while Hong Kong's Hang Seng declined 1.4%.
The main US share index was flat in early Tuesday trading, after ending Monday down 1.2%.
Jean-Francois Robin of French investment bank Natixis said: "We find ourselves at one of the worst moments of the European monetary crisis.
"The idea of a contagion from the Greek crisis to other eurozone countries like Italy and Spain is gaining ground."
'Effective solutions' Eurozone finance ministers also discussed on Monday how, and by how much, banks and other financial institutions could contribute to a new rescue package for Greece.
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What went wrong in the eurozone?
Speaking from Washington, IMF managing director Christine Lagarde said it was not yet ready to discuss terms for a second Greek bail-out.
"Nothing should be taken for granted," she said.
Meanwhile, Greece's Prime Minister, George Papandreou, called for a comprehensive solution to his country's debt problems.
"I thus believe it is time now to address our fundamental problems head on and produce a comprehensive package of solutions that clearly signals our determination not to see the European project further damaged or destroyed," Mr Papandreou said in a letter to Jean-Claude Juncker, chairman of the eurogroup of finance ministers.
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