FRANKFURT — Germany’s stature as an island of stability in the European debt crisis was shaken Wednesday when it fell far short of selling all the government bonds it put up for auction.

Investors are beginning to question whether there are any havens left in Europe after German bonds, which the government uses to raise money for operations, got a surprisingly bad reception. The sale — more than one-third of the bonds found no buyers — helped push down stocks and contributed to the atmosphere of fear that prevails among the countries, including Germany, that share the euro currency.

While analysts cautioned against reading too much into a single bond auction, the weak auction was at the very least a blow to the prestige of Germany, whose economic strength has enabled it to largely dictate how the euro region will cope with the debt crisis.

And there is a growing sense in the region that unless the European Central Bank and big euro members like Germany and France agree to take major action to prop up the region’s finances, the euro-currency union itself could start to crumble. The debt crisis has toppled five governments, including Italy and Greece, by raising those countries’ borrowing costs to dangerously high levels. And now the crisis is prompting many investors to pull money out of the euro region altogether.