MADRID — Spain’s ailing banking industry could need as much as 59.3 billion euros, or $76.4 billion, in additional capital, according to an independent banking assessment published on Friday. The report paves the way for Madrid to request bank rescue loans that European finance ministers have agreed to extend.


The number was within the range of previous estimates and well below the potential 100 billion euros, or $128.8 billion, in bailout money that Spain negotiated with other euro zone countries in June.


And of the 14 banks assessed by the consulting firm Oliver Wyman, half are not in need of emergency funds. These include Santander, BBVA and La Caixa, the country’s three largest financial institutions.


Presenting the report, Fernando Jiménez Latorre, the Spanish secretary of state for the economy, said at a news conference that Spain would probably soon request about 40 billion euros, roughly $50 billion, of the European bailout offer. The audit, he said, should end the debate among investors about whether the Spanish banking sector can survive the consequences of a decade of reckless property lending. After Spain’s real estate bubble burst in 2008, many of its banks found themselves holding growing numbers of loans in or near default.


The bailout negotiations, and the need for an audit to assess the extent of the damage, were prompted by the government’s seizure in May of Bankia, one of the biggest real estate lenders, and signs that several others were on the brink of collapse.


The latest findings “should remove all the doubts about the strength of the system,” Mr. Jiménez Latorre said. “The bulk of it is solid, and the problems are well identified.”


The European Central Bank and the European Commission both issued statements Friday applauding the audit and expressing support for Spain. “This is a major step in implementing the financial assistance program and toward strengthening the viability of and confidence in the Spanish banking sector,” the commission, the administrative arm of the European Union, said in its statement.


In Washington, Christine Lagarde, managing director of the International Monetary Fund, also issued a statement, which said in part, “I strongly support the authorities’ commitment to ensure that capital needs are met in a timely manner and that the weakest banks are dealt with effectively.”


Still unresolved, though, is an issue over which Spain has been wrangling with its European partners since June, involving the exact terms of the banking rescue. The Spanish government has argued, so far without success, that emergency loans should be channeled straight to the banks rather than through the government, which would add to Spain’s debt load. Spain’s credit rating has gradually been lowered by the main rating agencies, with Moody’s expected to deliver another blow to Madrid as early as this weekend.


The poor credit rating is one reason that the Spanish government’s borrowing costs have been higher than those of many other euro zone countries, which could pose an even bigger challenge for the government of Prime Minister Mariano Rajoy. Mr. Rajoy and his finance officials have been pondering whether to ask for help through a bond-buying program recently announced by the central bank, which in many ways was designed with Spain in mind.


The problem for Mr. Rajoy is the stigma of seeking assistance from the central bank program — along with the requirements for tougher fiscal discipline that might accompany the aid. He is already facing an increasingly restive public, and threats of secession by the economically powerful Catalan region, over the austerity budget measures his government has imposed.


And yet, the audit showed at least a potential exit path for Spain from its bank problems.


The independent report, which Oliver Wyman based on its own work and on audits from four other firms, indicated that the banks could need as much as 53.745 billion euros to be cleaned up, assuming that mergers and restructuring plans currently under way were completed. The figure would climb to 59.3 billion euros if those plans failed, the report said.


The audit confirmed the central role played by Bankia in Spain’s banking crisis, which peaked in early May with the government takeover. Bankia’s new board then asked for 19 billion euros to replenish its capital reserves, on top of the 4.5 billion euros it had already received from a government bailout.


According to the report, Bankia could need a slightly higher amount, as much as 24.7 billion euros, to meet required capital levels if Spain’s economy remained in recession.


Three other nationalized banks face a combined capital shortfall of 21.5 billion euros. Among the threatened institutions is Banco Popular, a big commercial bank that faces a shortfall of 3.2 billion euros, according to Oliver Wyman.


The findings were in line with a forecast the economy minister, Luis de Guindos, made in an interview last month, as well as with a preliminary assessment by Oliver Wyman, which estimated in June that Spanish banks needed 51 billion to 62 billion euros of extra capital.