BBC’s Stephen Evans said reaction in Europe is “shock and dismay”
The head of the European Parliament has demanded “full clarification” from the US over a report that key EU premises in America have been bugged.
Martin Schulz said that if this was true, it would have a “severe impact” on ties between the EU and the US.
The report, carried by Germany’s Der Spiegel magazine, cites a secret 2010 document alleging that the US spied on EU offices in New York and Washington.
Fugitive ex-CIA analyst Edward Snowden leaked the paper, Der Spiegel says.
Mr Snowden – a former contractor for the CIA and also the National Security Agency (NSA) – has since requested asylum in Ecuador.
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”.
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, the BBC’s Stephen Evans says.
In a statement on Saturday, Mr Schulz said: “On behalf of the European Parliament, I demand full clarification and require further information speedily from the US authorities with regard to these allegations.”
Der Spiegel also quotes 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.”
Mr 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, unauthorised communication of national defence information and wilful communication of classified communications intelligence.
Each charge carries a maximum 10-year prison sentence.
On Saturday, US Vice-President Joe Biden and Ecuadorian President Rafael Correa held a telephone conversation about Mr Snowden’s asylum request.
According to Mr Correa, Mr Biden had “passed on a polite request from the United States to reject the request”.
The left-wing Ecuadorian leader said his answer was: “Mr vice-president, thanks for calling. We hold the United States in high regard. We did not seek to be in this situation.”
If Mr Snowden ever came to “Ecuadoran soil” with his request, he added, “the first people whose opinion we will seek is that of the United States”.
Quito earlier said it was willing to consider Mr Snowden’s request but only when he was physically in the Latin American country.
Meanwhile, White House spokeswoman Bernadette Meehan said only that Mr Biden and Mr Correa had held a wide-ranging conversation.