BRUSSELS — Is the euro crisis back with a vengeance, or do investors have a needless case of anxiety?

Until very recently, the gloom over the Continent had seemed to be lifting, with the conclusion of Greece’s second bailout and the calming effect on the financial sector of cheap loans from the European Central Bank. But last week’s jump in borrowing costs for Spain and Italy provided a clear signal that the euro’s problems are far from solved.

“Financial strains in Europe have eased somewhat since December,” Christine Lagarde, director of the International Monetary Fund, said in a speech in Washington on Thursday. “However, events of the past week remind us that markets remain volatile and that turning the corner is never easy.”

The turn looks tightest in Spain, which is still under intense pressure from the European Union to narrow a gaping budget deficit and clean up its banking system after a housing bubble burst, even as the country slides back into recession, with roughly one in four workers unemployed.