Context. Circumstellar debris disks older than a few Myr should be largely devoid of primordial gas remaining from the protoplanetary disk phase. Tracing the origin of observed atomic gas in Keplerian rotation in the edge-on debris disk surrounding the similar to 12 Myr old star beta Pictoris requires more detailed information about its spatial distribution than has previously been acquired by limited slit spectroscopy. Especially indications of asymmetries and presence of Ca II gas at high disk latitudes call for additional investigation to exclude or confirm its connection to observed dust structures or suggested cometary bodies on inclined eccentric orbits. Aims. We set out to recover a complete image of the Fe I and Ca II gas emission around beta Pic by spatially resolved, high-resolution spectroscopic observations to better understand the morphology and origin of the gaseous disk component. Methods. The multiple fiber facility FLAMES/GIRAFFE at the Very Large Telescope (VLT), with the large integral-field-unit ARGUS, was used to obtain spatially resolved optical spectra (from 385.9 to 404.8 nm) in four regions covering the northeast and southwest side of the disk. Emission lines from Fe I (at 386.0 nm) and Ca II (at 393.4 and 396.8 nm) were mapped and could be used to fit a parametric function for the disk gas distribution, using a gas-ionisation code for gas-poor debris disks. Results. Both Fe I and Ca II emission are clearly detected, with the former dominating along the disk midplane, and the latter revealing vertically more extended gas. The surface intensity of the Fe I emission is lower but more extended in the northeast (reaching the 210 AU limit of our observations) than in the southwest, while Ca II shows the opposite asymmetry. The modelled Fe gas disk profile shows a linear increase in scale height with radius, and a vertical profile that suggests dynamical interaction with the dust. We also qualitatively demonstrate that the Ca II emission profile can be explained by optical thickness in the disk midplane, and does not require Ca to be spatially separated from Fe.