"It is understandable that the information that recently emerged raised concern," Lithuanian Foreign Minister Linas Linkevicius told AFP.
"However (...) I don't think that it is very productive to discuss media reports or classified documents that nobody has seen," he said in the capital Vilnius.
"Both strong political and economic EU-US ties must not be damaged."
A report in German weekly Der Spiegel detailed alleged covert surveillance by the US National Security Agency (NSA) of EU diplomatic missions in the United States and in Brussels.
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The European Union, Paris and Berlin have all called for answers following the latest spying claims attributed to fugitive leaker Edward Snowden.
EU Justice Commissioner Viviane Reding yesterday warned that negotiations with the United States towards a vast free trade zone could suffer a blow if the media reports proved true.
Linkevicius said the EU-US free trade talks were crucial to the economies on both sides of the Atlantic, and would remain a priority for the Baltic state's half-year presidency of the 28-member bloc.
"It would be best to let emotions die down and to deal with problems that arise constructively.