With the ECB review, the EU is trying to improve on two earlier reviews made under another agency, the European Banking Authority, in 2009 and 2011. Those reviews, or stress tests, lost credibility after some banks that had been given the all-clear later needed bailouts.
Fixing banks is seen as key to solving the debt problems afflicting the euro currency union and shoring up economic growth.
The ministers' statement repeated an earlier vague promise to have "national backstops" ready that didn't satisfy the ECB. It also went over a previously stated pecking order in case of bank losses: first, private money would be used to resolve the problem, and only then would governments use taxpayers' funds. Governments that could not afford the rescue could turn to the eurozone's bailout fund.
The finance ministers were also supposed to discuss how to create a centralized European agency that could order a bank anywhere in the region to be restructured or wound down. The agency would be backed by a fund that would be financed through a levy on banks.
Germany, the EU's biggest member, has said setting up the agency would require changing the basic EU treaty, which could take years, and said the EU instead should rely on a network of national bank rescue authorities.
The matter was expected to be contentious, and at one point, the ministers expected to work late into the night. In the end, Rimantas Sadzius, the Lithuanian finance minister who chaired the gathering, said he instructed a working group to look for a compromise, and the meeting broke up early.
"My general impression is despite quite popular stereotypes there is no polarization among member states," Sadzius said. He said finding a satisfactory formula for creating the agency by the end of the year "should be done, and it can be done."
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John-Thor Dahlburg contributed to this report.