Markets cheered the agreement, with the DAX in Frankfurt closing up 4.3 percent, Spain's Ibex up 5.7 percent and Italy's FTSE-MIB up a stunning 6.6 percent. The euro rose 2 percent to $1.2680 and borrowing rates for Spain and Italy dropped sharply.
Despite the market cheer, Merkel faced criticism in the media, where her hard-nosed approach to crisis management has been popular.
Under the headline "Merkel buckles," the Bild newspaper argued that the summit decisions "mark a turning point in crisis policy" and said that "Merkel gave up her hard position." The top-selling daily paper has been a cheerleader for a tough approach.
Leading news website Spiegel Online headlined a story on the summit: "The night in which Merkel lost," while Die Welt newspaper wrote of "Merkel's defeat in a historic night."
Still, Carsten Brzeski, an economist at ING in Brussels, noted that moves such as recapitalizing banks directly are still subject to some conditions and there was no immediate decision to help out Italy.
"The only real concrete decision taken ... is the start of a single bank supervision," he said. "In the end, the German principle of conditional integration is still intact."
"Short-term relief for Spain and Italy, however, remains very cryptic and limited," Brzeski said.
Analysts also noted that the amount of money available in the rescue fund, or ESM, is dwarfed by the amount of debt across the continent. Italy alone has outstanding debt of €2.4 trillion.
European leaders also agreed at the summit that bonds purchased by the rescue fund for Spain's bailout will no longer enjoy preferential treatment to other bondholders in case of a default.
Previously, they looked set to enjoy "senior" status, which had the unintended consequence of scaring private investors away. Merkel insisted that was a one-time move that won't affect future moves by the ESM.
And she made clear that her opposition to moving soon to jointly issued eurobonds remains unchanged. Experts say eurobonds would help weaker countries like Spain by spreading their debt risk across multiple countries.
But Germany worries about being exposed to that new debt and says eurobonds would remove pressure on weaker countries to reform their economies by cutting red tape, fighting tax evasion and lower business costs.
Leaders delayed their discussion of such long-term issues until October.
Van Rompuy and other senior EU officials had laid out a vision for the future make-up of the eurozone in a sweeping document presented before the summit. It includes share debt and giving up national powers over budgets to a central authority.
Juergen Baetz in Berlin contributed to this report.
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