In many ways their most important mission may be to quell their own infighting. The demand from France and others for bonds jointly issued by the 17 members of the euro currency union, to pool the borrowing risk, has grown louder, even as the opposition in Germany has grown more rancorous.

German officials said that Ms. Merkel, after arriving, met briefly with Greece’s caretaker prime minister, Panagiotis Pikrammenos. They said Ms. Merkel had told him Germany would do what it could to help Greece, but added as she has many times before that Athens would have to abide by the agreements it made with its lenders.

On June 17, Greece will hold a second round of elections that is being treated as a referendum on the loan agreement, and the date is evolving into a deadline for European leaders to offer some sort of hope to the Greek people. But it is not clear what form that might take.

The German central bank, the Bundesbank, warned in its monthly report Wednesday that the Greek situation was “extremely worrying,” but that easing Greece’s bailout terms “would damage confidence in all euro-area agreements and treaties and strongly weaken incentives for national reform and consolidation measures.”

Instead of euro bonds, less controversial measures, like increased financing for the European Investment Bank, the repurposing of existing European structural funds and even “project bonds” jointly issued for specific undertakings, are likely to be pursued. Spain’s prime minister, Mariano Rajoy, has called for more aggressive action by the European Central Bank.

Mr. Hollande has promised to find a way to generate economic growth not only in France but also for reeling economies like Greece. He has proposed that euro member nations pool their resources to make project bonds available for initiatives intended to promote growth. In the process, he has set himself as an opponent of Ms. Merkel and the austerity policies associated with her stance for fiscal rectitude.

Although the German and French finance ministers praised each other and spoke of their friendly and cooperative relations after their preliminary meeting in Berlin on Monday, the level of frustration in the German capital over Mr. Hollande’s vocal demand for euro bonds has become increasingly evident.