Italy's Monte dei Paschi bank, Austrian bank Raiffeisen, Spain's Banco Popular and two Irish banks have fared worst in EU-wide stress tests, the European Banking Authority said Friday.
The EBA said the results showed "resilience in the EU banking sector as a whole thanks to significant capital raising," but warned that results for individual banks "vary significantly."
"Whilst we recognize the extensive capital raising done so far, this is not a clean bill of health," Andrea Enria, the EBA's chairman said in a statement.
"There remains work to do."
The European Central Bank welcomed the results, saying the stress tests showed the "improved resilience" of the euro area banking system since the last tests in 2014.
The European Commission said the EU-wide stress-testing of 51 banks "confirms overall that banks are increasingly resilient."
The stress test's key barometer was the common equity tier 1 ratio, or CET 1, which measures a bank's readily accessible capital against its total assets.
A ratio of at least 7 per cent is normally considered secure, depending on the size of the bank and other factors.
The CET 1 ratio of ailing Monte dei Paschi was minus-2 per cent in the test of the banks' ability to withstand an economic shock in 2018, while Allied Irish Bank's ratio dropped to 4.3 per cent.
Banco Popular, the Bank of Ireland and Raiffeisen all had a CET 1 ratio below 7 per cent in the stress test, while UniCredit, Italy's largest bank, had a ratio of 7.1 per cent.
Reacting to the results, Allied Irish said the EBA test was "based on a 2015 static balance sheet and does not reflect current or future improved financial performance."
"AIB has undergone fundamental restructuring in recent years and is now sustainably profitable," the bank said, highlighting a reduction in impaired loans from 29 billion euros in December 2013 to 11 billion euros in June 2016.
The EBA launched the stress tests in February to assess the resilience of the EU banking system to shocks by examining 51 banks covering about 70 per cent of the EU's banking sector.
It included the results from 123 banks in its previous set of health checks in 2014, when 24 banks failed the test with a total capital shortfall of 24.6 billion euros (27 billion dollars).
The EBA said the lower number this year reflected its attempt to focus on larger banks, arguing that national bank watchdogs can test and monitor smaller banks.
No banks from Portugal and Greece were included in the stress test, and some analysts said they were disappointed with the scope of this year's exercise.
"We think it is a missed opportunity that the EBA 2016 stress tests will not be used to do a fuller and deeper health check of the banking system in Europe," Tomas Kinmonth, an analyst of European financial institutions at Dutch bank Abn Amro, said ahead of Friday's results.
"This is especially the case as in some countries the smaller banks are the least sound," Kinmoth said.