But giving a bailout to Cyprus is trickier than it seems. Cyprus’s politicians would prefer not to take European money, which comes with the harsh austerity conditions that have spread misery in Greece. And they can argue that Cyprus was doing relatively well until Greece’s second bailout, when Greek government bonds — of which Cypriot banks held piles — lost considerable value.

The question of keeping the euro together had seemed to be conveniently fading for Ms. Merkel, who in the fall put her full backing behind the euro zone, quieting fears of a breakup. But Berlin seems to have been caught off guard by the political tempest stirred up by Cyprus, which has been shut out of international bond markets for a year but has been kept afloat by a $3.5 billion loan from the Russian government.

With that money running out, Germany and its European partners have been locked in a fierce debate over whether and how to throw Cyprus a lifeline. The problem is, most of the money lost by Cypriot banks was Russian, and the worry is that most of the bailout money could wind up in the hands of Russian oligarchs and gangsters. That fear, backed by a recent report by German intelligence, has stoked a furor even among some of Ms. Merkel’s political partners. “I do not want to vouch for black Russian money,” Volker Kauder, a prominent member of her conservative bloc, said recently.

The Russian presence is thick on Cyprus, a picturesque Mediterranean island and a onetime British colony. The bustling, large city of Limassol has an enclave of restaurants, shops and fur boutiques so packed with Russians that locals call it “Limassolgrad.”

Officials in Cyprus say there is no proof that the Russian cash in its banks is of dubious origin, and they insist that they cracked down on money laundering before joining the European Union. The officials point to an evaluation by the Organization for Economic Cooperation and Development showing that Cyprus is compliant with more than 40 directives against money laundering.