BRUSSELS — In the face of pressure from the embattled euro zone countries Italy and Spain, European leaders agreed early Friday to use the Continent’s bailout funds to recapitalize struggling banks directly, cheering financial markets but prompting unease in Germany, whose taxpayers may face more risk.

Stocks and the euro opened strongly higher in Europe and rose all day — a clear suggestion that the summit, by breaking new ground, had exceeded expectations. Analysts cautioned that earlier summit agreements had prompted market rallies that proved short-lived.

The decision, by leaders of the 17-nation euro zone, would allow help to banks without adding directly to the sovereign debt of countries, which has been a problem for Spain and potentially for Italy. Both countries have seen the interest rates on their debt rise to levels that would be unsustainable in the long term, and the Italian and Spanish prime ministers, Mario Monti and Mariano Rajoy, came here to push their colleagues to help.

Though the German chancellor, Angela Merkel, made concessions, they came with conditions, and some of the detail remained unclear Friday, prompting calls for more clarity to be provided quickly.