BERLIN — The warning came to the German security authorities in early September from “our best partners,” as they euphemistically refer to the American intelligence agencies: A terrorist assault might be in the works.

In the weeks that followed, the Germans identified a suspect, a refugee from Syria. They unearthed evidence that he had been casing a Berlin airport for an attack, and they recovered powerful explosives from his apartment, only to see him slip through their fingers. When they eventually captured him, the suspect promptly hanged himself in his jail cell.

The case was notable for its dramatic turns. But it also underscored two central challenges facing the Continent: getting a handle on the security risk related to the arrival of more than a million migrants last year, and addressing the continued reliance of European governments on intelligence from the United States to avert attacks.

Both issues have been plaguing Europe since the high-profile attacks in France and Belgium over the past two years. Governments have scrambled to counter the threat even as migrants, many with little or no documentation of their identity or country of origin, came over their borders in previously unheard-of numbers. The challenge has become more pressing in Germany in recent months after a spate of arrests and attacks, some linked to migrants.