The purity of an optical vortex beam depends on the spread of its energy among different azimuthal and radial modes, also known as ℓ- and p-modes. The smaller the spread, the higher the vortex purity and more efficient its creation and detection. There are several methods to generate vortex beams with well-defined orbital angular momentum, but only few exist allowing selection of a pure radial mode. These typically consist of many optical elements with rather complex arrangements, including active cavity resonators. Here, we show that it is possible to generate pure vortex beams using a single metasurface plate—called p-plate as it controls radial modes—in combination with a polarizer. We generalize an existing theory of independent phase and amplitude control with birefringent nanopillars considering arbitrary input polarization states. The high purity, sizeable creation efficiency, and impassable compactness make the presented approach a powerful complex amplitude modulation tool for pure vortex generation, even in the case of large topological charges.