Millions of phone records at the center of a firestorm in Europe over spying by the National Security Agency were secretly supplied to the U.S. by European intelligence services—not collected by the NSA, upending a furor that cast a pall over trans-Atlantic relations.

The revelations suggest a greater level of European involvement in global surveillance, in conjunction at times with the NSA. The disclosures also put European leaders who loudly protested reports of the NSA's spying in a difficult spot, showing how their spy...