Updated

Emerging allegations that America's National Security Agency bugged and hacked European Union offices stoked tension Sunday between U.S. and European officials, with German prosecutors announcing they are probing the claims.

The allegations were carried in a report by the German magazine Der Spiegel. They are the latest claims to surface regarding NSA surveillance activity, as on-the-lam leaker Edward Snowden feeds a series of sensitive documents to the media. Der Spiegel did not specifically say how it obtained the information.

European Parliament President Martin Schulz, in response, demanded a clarification from the NSA about the alleged program.

"I am deeply worried and shocked about the allegations of U.S. authorities spying on EU offices," Schulz said in a statement, according to The Wall Street Journal. "If the allegations prove to be true, it would be an extremely serious matter which will have a severe impact on EU-U.S. relations."

German federal prosecutors also said they are looking into the reports. The Federal Prosecutors' Office said in a statement Sunday that it was probing the claims so as to "achieve a reliable factual basis" before considering whether a formal investigation was warranted.

It also said private citizens were likely to file criminal complaints on the matter.

A representative with the NSA referred questions on the matter to the Office of the Director of National Intelligence, which has not yet commented on the report.

But Michael Hayden, the former director of both the NSA and CIA, said Sunday that European officials should look in the mirror before criticizing the U.S.

"Any European who wants to go out and rend their garments with regard to international espionage should look first and find out what their own governments are doing," he said on CBS' "Face the Nation."

Hayden noted he's been out of the agency for years and said he didn't know the accuracy of the Der Spiegel report, nor could he confirm or deny it if he did.

But he said "the United States does conduct espionage," and that the Fourth Amendment right to privacy "is not an international treaty."

Der Spiegel reported that the NSA appears to have installed bugs in an EU building in Washington, D.C., as well as infiltrated their computer network. According to the report, this let U.S. officials monitor discussions and emails.

U.S. officials have warned that the string of NSA leaks are damaging to national security.

Snowden is believed to still be at the Moscow airport. Russian officials so far have refused to expel him to the U.S., claiming he is in a transit zone and not technically in their hands.

Meanwhile, Vice President Biden on Friday called Ecuador's president to urge the country to reject a request by Snowden for asylum in that country.

The Associated Press contributed to this report.