Ms. Merkel is preparing to head to Camp David in Maryland for the Group of 8 meeting beginning on Friday, and she is likely to be pressed there by the leaders of other industrial nations, in particular by President Obama, to find a way to quell the turmoil. On Tuesday night she met for the first time with France’s newly inaugurated president, François Hollande, who campaigned on the need for more growth-promoting policies.

In recent days Ms. Merkel has signaled a growing openness to additional growth measures as long as they do not interfere with the fiscal compact to cut deficits in the euro zone in the long run. “On the one hand we have the pillar of sound fiscal policy, and the second pillar will then be the growth component,” Ms. Merkel said in the CNBC interview.

That support could come in the form of money from existing European Union funds that would be redirected for use by crisis countries, said Fabian Zuleeg, the chief economist with the European Policy Center. That approach had been championed by Mr. Hollande.

But it will take more than technical adjustments to calm the growing political opposition to austerity in Greece, Spain and other hard-hit countries in the euro zone’s periphery, Mr. Zuleeg added. “We need to put together a package that looks convincing. It can’t just be rhetoric; it has to have some real elements to it,” he said. “The real element that certainly has to be in there is money.”

Ms. Merkel’s comments punctuated a day in which all sides — from European policy makers in Brussels to political operatives in Athens, where a caretaker government was named on Wednesday — began gearing up for a second Greek election, scheduled for June 17. The political establishment in Greece and elsewhere is seeking to describe the vote as a referendum on membership in the euro, which a large majority of Greeks say they support, even as they also demand a renegotiation of the terms of their bailout agreement.