The leaks from a secret BND report suggest that its monitoring station at Bad Aibling spied on France?s presidential palace and foreign ministry, and the European Commission.
The US National Security Agency also allegedly spied on some European firms.
German Interior Minister Thomas de Maiziere denies claims of a cover-up.
The BND reportedly collected information on European firms at Washington?s behest to check if they were breaking trade embargos.
According to the reports, the BND did not target German or US officials in the surveillance, as they are protected by a BND-NSA agreement signed in 2002.
However, it has emerged that the German government knew about NSA spying on European arms businesses as early as 2008. The government found ?shortcomings? in the BND?s operations, German TV reports.
Mr de Maiziere denies having had any knowledge of malpractice at German intelligence.
But he called for the internal BND report to be presented to a parliamentary committee, ?the sooner the better?.
The huge scale of NSA surveillance in Europe ? including joint spying operations with the UK?s GCHQ ? was revealed in 2013 by US whistleblower Edward Snowden.
There was outrage in Germany because of the scope of NSA spying, which allegedly included snooping on Chancellor Merkel?s mobile phone conversations. The revelations strained German-US diplomatic ties.
Last July Germany expelled a CIA official based at the US embassy, as reports surfaced of several Germans having spied for the NSA.
Germany?s leftist Die Linke party accused the German government on Wednesday of ?lying? in connection with NSA activities.
German media reports speak of NSA attempts to spy on Airbus and Eurocopter, now known as Airbus Helicopters, via the BND.