(Repeats Sept 30 story with no changes to text)
By Laura Noonan, Lefteris Papadimas and Eva Taylor
LONDON/ATHENS/FRANKFURT, Sept 30 (Reuters) - Greece has won an important concession from the European Central Bank (ECB) that could help its top four lenders pass a landmark review of the euro zone's banking sector, three sources familiar with the process told Reuters.
The sources said Greece had convinced the ECB to take into account the banks' restructuring plans in reaching its verdict on their finances, part of pan-European efforts to ensure banks are adequately structured in case of another financial crisis.
The ECB is testing whether banks have properly valued their assets and whether they have enough capital to withstand another financial crisis without taxpayer bailouts. The results will be announced on Oct. 26, before the ECB becomes the euro zone's banking supervisor on Nov. 4.
Greek officials had been pushing the ECB since July to row back from its original stance that the tests, covering 131 of the euro zone's largest lenders, would only consider the impact of restructuring plans if they had been agreed with the European Commission by December 2013.
That was problematic because the latest restructuring plans of Greece's four largest banks, who were recapitalised twice amid their country's brutal six-year recession, were not agreed with the European Commission until June.
But the sources said the ECB had in recent weeks agreed to extend the deadline and take account of recently-agreed plans by Piraeus, National Bank of Greece, Alpha Bank and Eurobank.
The ECB previously said banks with eligible restructuring plans would be judged on a "dynamic balance sheet" basis, which considers the mitigating effects of asset sales and other promised measures, over the three years of economic shocks the ECB is testing the banks against.
"They've promised to disclose a summary of the dynamic balance sheet and take it into consideration," a source familiar with the discussions said. "They may well take into account the dynamic balance sheet when calculating the capital shortfall."
A Greek official confirmed the details and said other euro zone banks in similar positions might get similar treatment. Banks with plans agreed before the end of 2013 include Germany's Commerzbank and Italy's Monte dei Paschi,
A third person familiar with the process confirmed the deadline had been extended.
"Banks with restructuring plans approved before year-end 2013 will be doing stress tests based on a dynamic balance sheet," the ECB said.
"Banks with restructuring plans approved and signed off after the end of 2013 will be doing stress tests based on both static and dynamic balance sheets," it added.
It declined to elaborate on which would count for any capital requirements banks might have. The Bank of Greece declined to comment.
The European Banking Authority (EBA), which is co-ordinating the stress tests across the EU's 28 countries including the euro zone's 18, said: "Supervisors ... can of course decide to consider restructuring plans when assessing vulnerabilities and capital needs which will emerge from the stress test."
Greece has already helped its banks to pass the tests by introducing an accounting manoeuvre that allows them to convert sp-called deferred tax assets into tax credits, giving the banking sector a 2.5 billion euros ($3.2 billion) boost in core capital by 2015-2016.
Its bank bailout fund, the HFSF, has 11.4 billion euros left from an initial 50 billion set aside to rescue struggling banks, but Greek officials are loathe to allocate the banks any more cash.
Investors' estimates vary widely on the total capital shortfall among the banks being tested by the ECB and the 124 banking groups being reviewed by the EBA. On Tuesday, EBA chairman Andrea Enria told reporters in Vienna there would be some failures to pass the tests. (1 US dollar = 0.7917 euros) (Editing by David Holmes)