Spain's banks need €53.75 billion ($69.23 billion) in new capital, an independent audit showed, a figure below initial estimates that provides a benchmark for the cleanup cost of the ailing sector, the government and the Bank of Spain said Friday.

The number was lower than an €62 billion initial estimate Spain gave in June, providing some welcome news to the government of Primer Minister Mariano Rajoy which this week announced a series of spending cuts ad tax increases in an effort to stabilize the economy amid protests and political challenges from the country's richest autonomous region.

The European Commission welcomed the results, calling them "a major step" in restoring confidence in the country's banking sector. In a statement the commission said the report should allow the recapitalization of the first group of Spanish banks to take place on time in November.

The figure resulting from the audit will form the basis for the calculation of how much Spain will need to draw from a €100 billion credit line obtained from the European Union. Mr. Rajoy said before the results were released that the amount would be "far below the €100 billion" that was provisionally agreed to by the European Union.

The banking stress tests done by U.S. consultancy Oliver Wyman, under the supervision of a steering committee that includes representatives of the European Central Bank and European Commission, showed that seven banks need to boost their capital buffers, while the remaining seven are adequately capitalized in an adverse economic scenario.

A new state-owned "bad bank" will reduce final capital needs, while some banks will be able to plug capital holes on their own, without recourse to state aid.

As expected, the three banks that were nationalized over the past year had the biggest capital shortfalls. Bankia SA BKIA.MC -1.52% alone needs €24.74 billion, the Bank of Spain said in a statement, while Novagalicia Banco needs €7.18 billion and Catalunya Bank needs €10.83 billion.

Among the listed banks, Banco Popular Español SA POP.MC -2.58% was found to need €3.22 billion. In a statement sent to Spain's stock-market regulator, Banco Popular said it wouldn't need state aid.

Spain's three largest banks—Banco Santander SA, SAN.MC -2.13% Banco Bilbao Vizcaya Argentaria SA BBVA.MC -1.88% and CaixaBank SA CABK.MC -1.55% —won't need to raise new funds. Four smaller lenders are also off the hook: Banco de Sabadell SA, SAB.MC +0.97% Bankinter SA, BKT.MC +4.65% Kutxabank and Unicaja.