MEPs on Thursday voted to open an inquiry into the allegations that the United States spied on EU offices.
A total of 483 voted for the resolution, 98 against, and 65 abstained on the motion.
US whistleblower Edward Snowden has applied for asylum in nine EU countries. Seven have turned down his request, citing technicalities.
Two more — Germany and France — have not yet responded.
Liberal leader Guy Verhofstadt told euronews that it was wrong to place all the blame on Snowden.
“He just made things public that are not acceptable for us Europeans. That we are spied on by our enemies, yes! But not by our friends,” he said.
But one German centre-right parliamentarian warned the snooping row should not scupper free trade talks that are due to start next week.
Manfred Weber said: “We must not overlook the fact that this is also in the European Union’s strategic interests: Half of young people in Southern Europe are without work and so growth and jobs are strategic interests for the European Union. “
The first round of discussions between the EU and the US on a transatlantic trade pact are due to start in Washington on Monday.