BERLIN — After angrily insisting for months that “friends don’t spy,” the German government struggled Monday to respond to news media reports that its intelligence services routinely spy on Turkey, a NATO ally, and inadvertently captured at least one conversation each involving Hillary Rodham Clinton when she was secretary of state and her successor, John Kerry.

While officials in Berlin sought to play down the reports, Turkey summoned the German ambassador to demand an immediate investigation. “If there is even a bit of truth in these allegations, this is a grave situation that requires an explanation by Germany,” Turkey’s Foreign Ministry said in a statement.

In a tone of outrage heard repeatedly from politicians in Berlin over the past year when addressing widespread allegations of spying by the United States’ National Security Agency, the Turkish government demanded that German authorities “present an official and satisfactory explanation to the allegations,” adding that “if true, these practices should be terminated at once.”

Turkey remains on a list of countries targeted by Germany’s foreign intelligence service that was drawn up in 2009 and remains relevant today, the German magazine Der Spiegel reported on Monday, attributing the information to documents leaked to the Central Intelligence Agency. The magazine also reported that the German foreign intelligence service, known by its initials, BND, had captured individual conversations of Mrs. Clinton and Mr. Kerry while they were in the Middle East.