Spain submitted nearly all its banks to the tests, unlike other European countries, said EBA Chairman Andrea Enria in an interview with El Pais newspaper published on Sunday.
"It's a formidable exercise in transparency, which has not unveiled any great surprises and therefore I do not expect a black Monday. Absolutely not," said Enria.
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However, the five banks that failed the tests would need additional capital and a plan will be put in place to plug this gap, with measures discussed at a European level, he said.
The five banks that failed the tests account for less than 10 percent of the Spanish banking system. Four are unlisted regional savings banks and the other is small listed lender Banco Pastor
The additional capital outlined by the EBA for the five banks to reach a 5 percent core Tier 1 capital benchmark is 1.6 billion euros ($2.26 billion), according to test releases.
More than a quarter of the banks that took part in the tests were Spanish. Spain's two biggest banks, Santander
The five Spanish banks failed the tests because so-called generic provisions were not taken into account as capital. These provisions are a particularly Spanish measure and the regulator wanted to compare all banks on an equal footing.
Generic provisions are a method of building up a buffer during good times to protect against bad times. The Bank of Spain has been widely praised for this provisioning.
Bank of Spain Governor Miguel Angel Fernandez Ordonez said on Friday no Spanish bank needed additional capital as a consequence of the stress tests.
The EBA recommends the failed banks take measures to raise capital, Enria said.
"Now a plan must be put in place which will be discussed at a European level and I'm sure the Spanish authorities will do everything possible to rectify the capital shortfall identified in the tests," Enria said.
The Bank of Spain has said the state-backed bank restructuring fund, the FROB, is available for any additional capital holes identified by stress tests.
(Reporting by Sonya Dowsett; Editing by David Hulmes)