MADRID — Europe offered Spain a lifeline Saturday to rescue its deeply indebted banks, after Madrid begrudgingly acknowledged that it would become the fourth and largest Eurozone government to seek aid to contain the continent’s debt crisis.

After a three-hour video conference with fellow Eurozone finance ministers, Spanish Economy Minister Luis de Guindos signaled his government’s intention to request assistance from Europe’s rescue fund, already depleted by bailouts to Greece, Ireland and Portugal.

“The Spanish government declares its intention to solicit European financing to recapitalize Spanish banks that need it,” De Guindos told reporters at a hastily organized news conference in Madrid. The money would go directly intoSpain’sown bank rescue fund, which has only about $6 billion left, far short of the tens of billions needed to bolster several failing Spanish banks.

The Europe-wide fund will provide Spain with up to about $125 billion.

It was an about-face for a government that for weeks has vehemently denied that it might join the ranks of the bailed-out. About 24 hours before the request finally came, Deputy Prime Minister Soraya Saenz de Santamaria denied that EU ministers were even planning a conference call Saturday.

In a statement Saturday, those finance ministers said Spain’s formal request would be filed “shortly,” to be followed by agreements over conditions to which Spanish banks would be held. Even though the aid will go directly to Spanish banks, the government in Madrid “will retain the full responsibility” for paying back the loan, the statement said.

Officials of the European Union and its paymaster, Germany, are believed to have been eager to patch up Spain’s banking weaknesses before Greek elections June 17. Left-wing parties opposed to terms of the country’s EU bailout could win a majority in the Greek Parliament, throwing the country’s membership in the Eurozone into question. Any possible run on Spanish banks at the same time would severely strain Europe’s monetary union.

The Obama administration has urged Europe to tackle its banking problems, and U.S. Treasury SecretaryTimothy F. Geithnerwelcomed Saturday’s move, calling it “important for the health of Spain’s economy” and an indication that Europe was taking “concrete steps on the path to financial union.”

De Guindos was careful to avoid the word “bailout.” But if Madrid accepts the full amount on offer its rescue would be larger than previous bailouts for Portugal and Ireland, though less than half the size of Greece’s two loans combined.

“What we are asking is financial support, and this has absolutely nothing to do with a full bailout,” De Guindos said. Spain will specify exactly how large a loan it plans to accept after the results of independent bank audits come back June 21, he said.

De Guindos said that because the European loan would be earmarked only for recapitalizing Spanish banks, his government would not be subject to additional austerity measures. With and unemployment rate of nearly 25%, the Spanish public is wary of additional spending cuts or tax increases that outside oversight might have required.

Spain is believed to have been eager to minimize the role of the International Monetary Fund. IMF head Christine Lagarde listened in on the Saturday conference call, and ministers said in their statement afterward that the IMF was invited to “support the implementation and monitoring” of the loan to Spain. But the full amount would be drawn solely from the European rescue fund, and not from IMF coffers.

The loan’s terms are “much more favorable” than what Spain is able to raise on financial markets on its own, De Guindos said. For weeks, Spain’s borrowing costs have been hovering near levels that led Greece, Portugal and Ireland to seek bailouts.

Although Spanish government debt is relatively low compared with those nations, Spain’s banks are its economy’s weakest link, weighed down by unpaid mortgages and construction loans left over from the housing bubble. The fear is that without outside assistance, Spain’s banking sector will sabotage the national economy and destabilize the Eurozone as a whole.

Madrid had struggled to prop up its failing lenders on its own. It agreed to nationalize the country’s largest real estate lender, Bankia, to the tune of $24 billion in taxpayer money. But with its own rescue fund drying up and borrowing costs prohibitively high, the country apparently ran out of options.

The European Commission recently recommended that Spain tap continental rescue funds to fill the gap. The commission’s president, Jose Manuel Barroso, issued a statement late Saturday commending Spain on its move.

“With this thorough restructuring of the banking sector, together with the ongoing determined implementation of structural reforms and fiscal consolidation, we are certain that Spain can gradually regain the confidence of investors and market participants and create the conditions for a return to sustainable growth and job creation,” Barroso said in a joint statement with the commission’s vice president, Olli Rehn.

Frayer is a special correspondent.