Updated to include Eurogroup commentary. NEW YORK ( TheStreet) -- Fragile European banking conglomerates are facing a stress test of their own, after European officials offered a $13 billion bank bailout plan to Cyprus that's created risks of depositor flight. The terms of the bailout and investor skepticism may test whether EU-based banks have the financial strength to withstand a return to economic stress, or whether difficulty in raising capital keeps regional lenders in a vulnerable position . The Eurozone banking sector fears come just a week after the Federal Reserve gave U.S. lenders a relatively clean bill of health on stress tests, which sought to check that banks would have the capital to withstand a new financial downturn. A crisis scenario may be developing in Europe, on the heels of Cyprus' harsh proposed bailout. Eurozone finance ministers agreed Saturday on a bailout plan for Cyprus that requires a levy of a 9.9% tax on bank accounts with balances above EUR100,000 and those with less that amount to be taxed at a 6.75% to raise EUR5.8 billion for the near-bankrupt nation. The tax on large deposits has been taken by economists as a bail-in of hot money Russian bank accounts in Cypress, while the tax against smaller accounts may prove more problematic for depositor confidence throughout the EU. Both taxes have created fears of a run on the island-nation's banks and raises concerns that similar moves in countries like Italy could push the European banking system back into a state of emergency. Since the European Central Bank offered nearly $1 trillion in guarantees to buy EU government bonds in the fall of 2011, pressures on the balance sheets of regional lenders and peripheral nations have fallen sharply. Through the day Monday, markets reversed from early losses to gains as investors questioned whether the bailout terms would have wider ramifications. Late on Monday the Eurogroup said it might reconsider the extent of depositor levy. "The Cypriot authorities will introduce more progressivity in the one-off levy compared to what was agreed on 16 March, provided that it continues yielding the targeted reduction of the financing envelope and, hence, not impact the overall amount of financial assistance up to EUR 10bn," the Eurogroup said in a statement. "The Eurogroup continues to be of the view that small depositors should be treated differently from large depositors and reaffirms the importance of fully guaranteeing deposits below EUR 100,000." On Tuesday Cyprus' will vote on whether to approve the country's bailout package, which could help the country stave off default. After incorrectly betting on the debt of peripheral nations like Greece, Cypriot banks have put the country's finances at risk of total collapse because of their size relative to gross domestic product. "The depositor levy also has negative implications for European bank creditors," Bart Oosterveld, a managing director of sovereign risk at Moody's, wrote in a late Sunday note. The preference by EU officials to impose losses on senior creditors such as depositors over taxpayer supported guarantees may create risks to the region's overall financial system, Oosterveld noted. " The decision to impose losses on depositors signals euro area policymakers' willingness to risk triggering wider financial market disruptions in pursuit of other policy goals," wrote Oosterveld, who notes a "significant departure" from bailouts of Spanish and Dutch lenders that targeted only junior creditors. Depositors in Cypriot banks will incur losses of nearly EUR6 billion, imposed via a 'one-off levy,' which Moody's said it would classify as a default. As investors await further details of the deal and whether the Cyprus parliament will even accept the deal, the prospect of depositor losses may already be creating a stressed scenario for European banks. Shares in Deutsche Bank ( DB) were off over 3%, while Santander ( SAN) and Banco Bilbao Vizcaya Argenteria ( BBVA) were trading lower by a similar percentage Monday. JPMorgan analysts said in a Monday note terms of the Cypriot bailout signal an EU-wide deposit guarantee, similar to that imposed in the U.S. by the Federal Deposit Insurance Corporation is now less likely.