During the 2008-12 financial crisis euro zone countries paid billions of euros to rescue failing lenders who were exposed to risky financial products.
"There is still lots to be done to make sure that we are in the best possible position to resolve a failing bank," EU Financial Services Commissioner Jonathan Hill said on Friday before praising the progress achieved since the last financial crisis in making the European banking system more stable.
A key new instrument to prevent banking crisis is the upfront drafting of resolution plans for the main euro zone banks, so that when a lender is on the verge of collapse it can be rescued in a short timeframe, ideally in a weekend.
The Single Resolution Board, a new EU banking body, is in charge of preparing these plans but only some of them are already available.
"We have come a long way, but we are not there yet. We do not have these plans yet for all banks, but we are getting there," SRB member Joanne Kellermann told a conference on Friday.
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The head of the economic affairs committee of the European Parliament Roberto Gualtieri urged the SRB to have resolution plans ready by the end of the year for all banks under its remit.
Kellermann said she was confident that plans will be ready for the majority of major euro zone banks, assuring that the SRB would be able to deal with possible crisis, if they emerged.
As part of the banking union, euro zone states have agreed on common supervision of the bloc`s banks and have set up the Single Resolution Fund (SRF) to rescue ailing lenders, but have failed to agree on a financial backstop to support the SRF in its early years.
"We need to provide a credible long-term backstop for the single resolution mechanism," Hill said.
In a document addressed to EU finance ministers in April, France and Italy have called for the euro zone bailout fund, the European Stability Mechanism, to provide financial support to the SRF. The ESM has a lending capacity of 500 billion euros.
Euro zone countries are also divided on setting up a European deposit insurance scheme (EDIS), designed to be the third and last pillar of the banking union.
National deposit insurance schemes are in place in EU states to underwrite savings of up to 100,000 euros ($114,040) if domestic lenders fail, as required by EU rules.
But national schemes may prove insufficient to deal with multiple failures.
"EDIS would make banks better protected if there were larger local shocks," Hill said.
Despite strong backing from all EU institutions and many states, the plan is not taking off because of German opposition, as Berlin fears that its wealthier deposit guarantee funds may be used to rescue savers in other countries.
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