France and Germany are urging the United States to come clean over claims that its intelligence services have been spying on key EU offices.
A report in Germany's Der Spiegel magazine said European Union 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 ex-CIA analyst Edward Snowden is said to be the source of the leaks.
Mr 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.
'Cold War' behaviour
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 behaviour was reminiscent of the Cold War.
"If the media reports are accurate, then this recalls the methods used by enemies during the Cold War," he 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 British newspaper 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, the BBC's Stephen Evans says.
There was particular concerns over claims a building used by ministers in Brussels had its phones tapped and internet hacked by US security services, our correspondent adds.
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."
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.
Mr Correa told the news agency Reuters on Sunday that Mr Snowden's fate was in the hands of the authorities in Russia. Ecuador could not consider Mr Snowden's asylum request until he had arrived in the Latin American country, he said.
"It's up to the Russian authorities if he can leave the Moscow airport for an Ecuadorean embassy," he was quoted as saying.
"He will be treated just like any other citizen even though he does not have a passport. We are clear that this is a special situation."
Mr Correa added that his country continued to support Wikileaks founder Julian Assange, who has been sheltering in its London embassy for a year.
In an interview with ABC television, Mr Assange dismissed remarks by US Secretary of State John Kerry that people could die as a result of Mr 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.
20 May: Snowden flies from Hawaii to Hong Kong.
5 June: From Hong Kong, Snowden discloses details of what he describes as a vast US phone and internet surveillance programme to the UK's Guardian newspaper.
23 June: Snowden leaves Hong Kong on a flight to Moscow. He is currently thought to remain airside at Sheremetyevo airport.
From Moscow, Snowden could fly to Cuba, en route to Ecuador, which has said it is "analysing" whether to grant him asylum.
Venezuela had also been considered a possible destination for Snowden, however it is thought he would only pass through on his way to Ecuador.
Snowden is reported to have requested asylum in Ecuador, which previously granted haven to Wikileaks founder Julian Assange in its London embassy.