The European Central Bank, poised to take over supervision of the region's banks, said on Friday there was no room for complacency following early signs of easing strain on financial markets.
It urged governments to push ahead with reforms.
Tension in euro zone debt markets has eased since ECB President Mario Draghi pledged in July to do whatever it takes to preserve the euro but some risks prevail.
Putting the ECB in charge of supervising the larger euro zone banks is an important step to make the bloc's institutions more crisis resilient, but more needs to be done to avoid a renewed crisis flare-up, the ECB said.
"The situation is still very fragile in many ways," ECB Vice-President Vitor Constancio told reporters at a presentation of the bank's twice-annual Financial Stability Review.
"Key financial stability risks remain and there is no room for complacency," the ECB said in the report.
The main risks are a possible renewed intensification of the crisis if governments fall behind on their reforms, a deterioration of banks' health and further funding strains as money and debt markets are still not functioning properly.
Although banks faced lower refinancing needs next year than this year, there was still a lot of pressure because of funding restrains and higher capital requirements, Constancio said. But he also said that a new set of tougher banking standards on capital and liquidity, known as Basel III, would not be implemented in 2013, which would give banks more time to adapt.
"The implementation will not be in 2013, because there were delays in the final definition of the liquidity ratio," he said.
His ECB colleague, Joerg Asmussen, also noted the risk that an easing of financial market pressure could encourage policymakers to take their foot off the gas.
"The work on (reform efforts) must be continued vigorously," he told Reuters.
The banking union -- a three-part process which involves creating a single supervisor, establishing a fund to wind down problem banks and fully coordinating national schemes that guarantee deposits -- is seen as key to address such risks.
Following months of negotiations, EU finance ministers agreed on Thursday to hand the ECB authority to police directly at least 150 of the euro zone's biggest banks and to intervene in smaller banks at the first sign of trouble.
"Those 150 banks represent 85 percent of total assets in the euro area ... which I would say is more than enough," Constancio said, adding that the single supervisory mechanism had legal competence over all euro zone banks.
But Jens Weidmann, head of Germany's Bundesbank and member of the ECB Governing Council, suggested EU finance ministers should have given the ECB oversight of fewer euro zone banks.
"One could have drawn the circle of systemically relevant banks a little bit tighter," Weidmann was quoted as saying by German magazine Wirtschaftswoche. "I'm not convinced that the ECB Governing Council is the ideal body to decide whether a bank should be closed or not."
The next step is to establish a fund to wind down troubled banks, which Constancio said should be modeled on the U.S. Federal Deposit Insurance Corporation (FDIC).
"This is not about creating a European fund with big amounts of money to use for resolution," Constancio said. "You can look to the example of the U.S., where the FDIC does this task."
The FDIC had dealt with more than 400 troubled banks since 2008 without using public money, Constancio said, adding that the resolution mechanism should not be used to bail out banks, which was the responsibility of governments.
"It's about bail-in -- it's not about bailout -- in order to minimize any possible contribution of public money to the resolution of banks. That's one of the lessons of the crisis," Constancio said.