MADRID — Conservative Spanish Prime Minister Mariano Rajoy insisted Monday that the country’s banking sector would not need an international rescue as concern over the bailout of nationalized lender Bankia sent its stock price plummeting while Spain’s borrowing costs soared.

“There will be no rescue of the Spanish banking sector,” Rajoy told a press conference.

However, he added that the government had no choice but to bail out Bankia, which has been crippled by Spain’s real estate slump.

“We took the bull by the horns because the alternative was collapse,” said Rajoy, stressing that Bankia clients’ savings were now safer than ever.

Bankia, Spain’s fourth-largest bank, is estimated to have 32 billion euros in toxic assets and was effectively nationalized earlier this month when the government converted 4.5 billion euros in rescue funds it gave last June into shares.

The lender’s shares fell 28 percent on opening in Madrid on Monday — Bankia’s first day back on the stock exchange following its announcement Friday that it would need the $23.8 billion in state aid to shore itself up against its bad loans, a far bigger bailout than expected. The shares, which recovered slightly in the afternoon, closed 13.4 percent lower at 1.36 euros.

Bank of Spain estimates show Spain’s lenders are sitting on some $233 billion in assets that could cause them losses. The government fears the cost of rescuing the country’s vulnerable banks could overwhelm its own finances, which are already strained by a double-dip recession and an unemployment rate of nearly 25 percent, and force it to seek a rescue by the rest of Europe.

Among the chief concerns surrounding Bankia’s request for state aid — the largest in Spanish history — is just how Spain plans to fund it. The country’s borrowing costs have risen sharply over the past few weeks.

On Monday, Spain’s interest rate, or yield, for 10-year bonds on the secondary market — a key indicator of market confidence — rose 0.16 percentage points to close at 6.45 percent. Rajoy dismissed suggestions it had anything to do with Bankia.

A rate of 7 percent is considered unsustainable over the long term, and there is concern that Spain might soon be pushed to seek an international bailout.