Leopoldo Lopez and Antonio Ledezma, the South American nation's highest profile leaders of the opposition to President Nicolas Maduro, were both already under house arrest when they were picked up by the Venezuelan intelligence service.
"A few weeks ago we had welcomed the transfer of Leopoldo Lopez from his prison into house arrest," Catherine Ray, a spokeswoman for EU diplomatic chief Federica Mogherini, told a daily briefing when asked about the detention of the two men.
The EU yesterday said it had "grave doubts" about recognising the vote, and today it again urged the government in Caracas to end a four-month crackdown on protests that has left more than 120 people dead.
"We keep calling the government of Venezuela to work towards urgent confidence-building measures aimed at de- escalating the tensions and fostering better conditions for resuming efforts towards a peaceful negotiated solution," said Ray.