European nations have made concessions in recent weeks to boost confidence in an upcoming rescue of the Spanish banking system, and the country’s politicians have forged ahead with plans to control government deficits.

But world markets seemed unimpressed Thursday, when a Spanish bond auction produced a disturbing jump in interest rates and intensified speculation that the euro area’s fourth-largest economy can’t survive without outside help.

Thursday’s bond auction left Spain paying nearly 7 percent for its seven-year bonds — a level that would be difficult to sustain and one that has pushed other European countries into international bailout programs. The rate was a full two percentage points more than in the country’s prior bond auction.

The outcome of a single, small bond sale isn’t necessarily a final verdict. The country sold a little more than $3 billion in bonds on Thursday and has raised most of the money it needs for the year.

A statement from the Spanish government focused on the fact that buyers had been willing to purchase about $7 billion in government debt, a sign that demand remains healthy and markets are still willing to fund the Spanish state.

But it was a worrying development after weeks in which European officials made what they regarded as important progress toward a broad restructuring of the 17-nation euro currency union. They had also improved the terms of the Spanish bank rescue to build faith that the banks can be fixed without damaging the government’s credit standing.

That involved a series of concessions. European leaders agreed to put up as much as $120 billion to pay for the bank rescue, and they agreed to change the rules for a regional rescue fund so that it could lend money directly to the banks and not run up the Spanish government’s debts. They also agreed that the bank rescue loans would not take precedence over other debts that the banks may owe. That last concession was an important effort to reassure private investors, who worried that they would be the first to shoulder any losses. The program cleared an important hurdle on Thursday when it was approved by the German parliament.

But even with those concessions, and the announcement of new deficit cuts intended to show that the government is getting control of the country’s finances, Spain’s outlook remains clouded. Deposits continue leaving the country’s banking system, bad loans continue rising and an economic recession has compounded the downward spiral.

“No one can muscle up a plan to make those banks safe in the foreseeable future,” Carl Weinberg, chief economist at the High Frequency Economics consulting firm, wrote in an analysis. Weinberg concluded that Spain — and Europe as a whole — remains a long way from clarifying which of its banks will survive and which will fail, a necessary condition for stabilizing the euro zone.

“Depositors naturally take money out of banks that are unsafe,” he wrote. “Investors do not want to buy shares in failed banks.”

The International Monetary Fund this week expressed similar concerns, saying that Spain and Italy are both paying far higher interest rates than economic conditions in their countries would warrant.

Carlo Cottarelli, director of the IMF’s fiscal affairs department, said the premium may be as much as two full percentage points and is largely a result of doubt about the viability of the euro itself. Investors have pulled money out of the currency union or repatriated it behind national borders in a massive reshuffling of capital that has left banks in the hardest-hit countries struggling to say afloat and dependent on loans from the European Central Bank.

The ultimate solutions — essentially a renegotiation of the currency union’s underlying rules — will take years. The stress in bond and financial markets is a sign, Cottarelli said, that markets won’t wait that long.

The high rates in Spain and Italy “reflect the challenges that the euro project as a whole is facing,” said Cottarelli, who was among several IMF officials who suggested this week that the European Central Bank needs to intervene soon to hold down borrowing costs for those two countries.