The official EU body also found traces of pesticides in organic foods, though it said its analysis of almost 81,000 food samples found the risk of any negative impact on health was low.
But campaign groups said the data was worrying, especially in the cases where residues of more than one pesticide were found. They said the pesticides were mostly fungicides, which are possible carcinogens, and more research was needed into the implications of exposure to more than one.
The latest EFSA report, for 2013, found that almost 55 percent of the samples of food products in European Union and neighboring countries were free from detectable traces of chemicals.
The highest rate of exceeding limits was for strawberries (2.5 percent of the sample). They are especially sensitive to disease and so undergo considerable spraying with pesticides.
EFSA said it had tested for 685 pesticides in the 27 nations that belonged to the EU for all of 2013 (Croatia joined in that year), plus Norway and Iceland, and had found multiple residues in 27.3 percent of samples.