Grid cells in the medial entorhinal cortex (MEC) generate metric spatial representations. Recent attractor-network models suggest an essential role for GABAergic interneurons in the emergence of the grid-cell firing pattern through recurrent inhibition dependent on grid-cell phase. To test this hypothesis, we studied identified parvalbumin-expressing (PV(+)) interneurons that are the most likely candidate for providing this recurrent inhibition onto grid cells. Using optogenetics and tetrode recordings in mice, we found that PV(+) interneurons exhibited high firing rates, low spatial sparsity and no spatial periodicity. PV(+) interneurons inhibited all functionally defined cell types in the MEC and were in turn recruited preferentially by grid cells. To our surprise, we found that individual PV(+) interneurons received input from grid cells with various phases, which most likely accounts for the broadly tuned spatial firing activity of PV(+) interneurons. Our data argue against the notion that PV(+) interneurons provide phase-dependent recurrent inhibition and challenge recent attractor-network models of grid cells.