A report in Germany’s Der Spiegel magazine said EU offices in the US and Europe had been bugged.
Other “targets” included the French, Italian and Greek embassies in the US, according to leaked documents later mentioned by the Guardian newspaper.
Fugitive whistleblower Edward Snowden is said to be the source of the leaks.
Edward Snowden – who was also a contractor for the National Security Agency (NSA) – has since requested asylum in Ecuador. He is currently believed to be staying at Moscow’s airport.
On Sunday, French Foreign Minister Laurent Fabius said that if the allegations carried by Der Spiegel were confirmed, such US activities would be “totally unacceptable”.
German Justice Minister Sabine Leutheusser-Schnarrenberger said the alleged US behavior was reminiscent of the Cold War.
“If the media reports are accurate, then this recalls the methods used by enemies during the Cold War,” she was quoted as saying by the Associated Press news agency.
“It is beyond comprehension that our friends in the United States see Europeans as enemies.”
Meanwhile, the President of the European Parliament, Martin Schulz said he was “deeply worried and shocked” by the allegations.
He said any such spying could have a “severe impact” on ties between the EU and the US.
According to the document – which Der Spiegel says comes from the NSA – the agency spied on EU internal computer networks in Washington and at the 27-member bloc’s UN office in New York.
The document also allegedly refers to the EU as a “target”.
Meanwhile, the Guardian reported that – according to one leaked report – 38 embassies and missions had been targeted.
The Guardian said the list included the French, Italian and Greek embassies, as well as a number of other American allies, including Japan, Mexico, South Korea, India and Turkey.
It is not known what information US spies might have got, but details of European positions on trade and military matters would have been useful to those involved in negotiations between Washington and European governments.
There was particular concerns over claims a building used by ministers in Brussels had its phones tapped and internet hacked by US security services.
The European Commission, which plays a key role in trade talks, has asked Washington to investigate Der Spiegel‘s report.
“We have immediately been in contact with the US authorities in Washington DC and in Brussels and have confronted them with the press reports,” it said in a statement.
“They have told us they are checking on the accuracy of the information released yesterday and will come back to us.”
The US government has so far made no public comments on the allegations.
Der Spiegel quoted Luxembourg Foreign Minister Jean Asselborn as saying: “If these reports are true, it’s disgusting. The United States would be better off monitoring its secret services rather than its allies.”
Edward Snowden is believed to be currently staying at Moscow’s airport. He arrived there last weekend from Hong Kong, where he had been staying since he revealed details of top secret US surveillance programmes.
The US has charged him with theft of government property, unauthorized communication of national defense information and willful communication of classified communications intelligence.
Each charge carries a maximum 10-year prison sentence.
In an interview with ABC television, WikiLeaks founder Julian Assange dismissed remarks by US Secretary of State John Kerry that people could die as a result of Edward Snowden’s revelations.
“We have heard this rhetoric. I myself was subject to precisely this rhetoric two, three years ago. And it all proved to be false,” he said.
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