The weekly news magazine said the U.S. National Security Agency carried out the surveillance. Martin Schulz, president of the European Parliament, said he was "deeply worried and shocked about the allegations of U.S. authorities spying on EU offices."
Schulz said that if the allegations were confirmed "it would be an extremely serious matter which will have a severe impact on EU-US relations."
The U.S. government has defended its efforts to intercept electronic communications overseas by arguing that this has helped prevent terror attacks at home and abroad.
Parliament officials want an immediate investigation into the claims, and suggested that recently launched negotiations on a trans-Atlantic trade treaty should be put on hold.
Der Spiegel didn't publish the alleged NSA documents it cited nor say how it obtained access to them. But one of the report's authors is Laura Poitras, an award-winning documentary filmmaker who interviewed /*Edward Snowden*/ while he was holed up in Hong Kong.
The U.S. is seeking Snowden's extradition after he leaked documents to the Guardian that revealed the NSA's surveillance program. Ecuador President Rafael Correa said Sunday Snowden is "under the care of the Russian authorities" and can't leave Moscow's international airport without his U.S. passport.
The Associated Press contributed to this report.
