The reports also said the agency had listened to the phone calls of two U.S. secretaries of state - the kind of activity for which Chancellor Angela Merkel has criticized Washington.
Turkey summoned the German ambassador and called for a full explanation following a Spiegel magazine report that the BND foreign intelligence agency had been spying on Turkey for years and identified Ankara as a top surveillance target in an internal government document from 2009.
Turkey's foreign ministry described the weekend report as "absolutely unacceptable" if true.
"It is expected that the German authorities present an official and satisfactory explanation on the claims reported by German media and end these activities immediately if the claims are true," it said in a statement.
Berlin declined to comment about surveillance on Turkey or reports in Sueddeutsche Zeitung newspaper and two broadcasters that the BND had "accidentally" overheard phone calls by U.S. Secretary of State John Kerry and his predecessor Hillary Clinton.
Last October, after reports surfaced that the United States had been monitoring her mobile phone, Merkel said that "spying among friends is not at all acceptable".
Revelations by former U.S. intelligence contractor Edward Snowden of surveillance by the United States' National Security Agency (NSA) have increased mistrust of Washington in Germany.
In an unusually public spat between the close Cold War allies, Berlin asked the top U.S. spy in Germany to leave the country in July after the Germans unearthed a double agent at the BND who admitting passing documents to American agents.
The German opposition now accuses the government of hypocrisy. Greens party co-leader Simone Peter said it was "incomprehensible" that Germany should be "actively spying on allied states" after the outcry about the NSA's activities.
NJF/NJF