We present spectropolarimetric observations of internetwork magnetic fields at the solar disk center. A Fabry-Pérot spectrometer was used to scan the two Fe I lines at 6301.5 and 6302.5 Å. High spatial resolution (0.5") magnetograms were obtained after speckle reconstruction. The patches with magnetic fields above noise cover approximately 45% of the observed area. Such large coverage renders a mean unsigned magnetic flux density of some 20 G (or 20 Mx cm-2), which exceeds all previous measurements. Magnetic signals occur predominantly in intergranular spaces. The systematic difference between the flux densities measured in the two iron lines leads to the conclusion that, typically, we detect structures with intrinsic field strengths larger than 1 kG occupying only 2% of the surface.