But, Mr. Schäuble said, “If Germany took such a decision, that would not be a German problem, but a huge threat for Europe.”

The comments by Mr. Schäuble were a sign of how worried Berlin has become about the future of the Schengen system and whether Europe can muster an effective response to the crisis after Mrs. Merkel threw open Germany’s borders to migrants last year in a humanitarian gesture that earned her, and Germany, accolades.

While pointing out a real danger, Mr. Schäuble’s comments appeared to amount to less of a threat than an attempt to spur action from European Union partners to help reduce the flow of refugees and migrants to Europe.

The comments came after it emerged on Friday that Italy was holding up a plan for the 28 European Union member states to contribute 3 billion euros, about $3.2 billion, to Turkey in order to help its government improve the conditions of the refugees living there. In turn, Ankara is supposed to do more to stop migrants from attempting to reach the Greek coast, which is a common arrival point for migrants who move north in the hope of gaining asylum in countries like Germany and Sweden.

Italy, which wants more flexibility from Brussels about its ability to manage its national budget, has demanded that the money for Turkey come from the European Union’s central budget.