REUTERS - German security agents recorded a conversation involving Hillary Clinton while she was U.S. Secretary of State, media reported on Friday, a potential embarrassment for Berlin which has lambasted Washington for its widespread surveillance.

Clinton's words were intercepted while she was on a U.S. government plane, Germany's Sueddeutsche Zeitung newspaper and German regional public broadcasters NDR and WDR said, without giving details of where she was or when the recording was made.

The respected broadsheet quoted German government sources saying the conversation had been picked up "by accident" and was not part of any plan to spy on Washington's top diplomat. The fact the recording had not been destroyed immediately was "idiocy", said one of the sources.

Both Germany's government and a spokeswoman for the National Security Council at the White House declined to comment on the reports on Friday.

Relations between the United States and Germany were hit last year by revelations by former U.S. National Security Agency (NSA) contractor Edward Snowden that Washington spied on German officials and bugged the phone of Chancellor Angela Merkel.

The dispute was revived in July when Germany's Federal Prosecutor arrested Markus R., a 31-year old employee of Germany's foreign intelligence agency (BND), on suspicion of spying for the Americans.

Details of the German recording of Clinton's conversation were included in documents that Markus R. had passed on to Washington, said the German media reports, without citing a source for that information.

The newspaper and the radio stations said a joint investigation had discovered the documents also showed Germany's government had ordered the BND to spy on a NATO partner state, without naming the country.

The media reports said U.S. authorities had brought up the affair in recent discussions, including one between current Secretary of State John Kerry and German Foreign Minister Frank-Walter Steinmeier.

Merkel said in an interview last month that the United States and Germany had fundamentally different conceptions of the role of the intelligence service, and she stressed the Cold War was over.