A representation of partially spatially coherent and partially polarized stationary electromagnetic fields is given in terms of mutually uncorrelated, transversely shifted, fully coherent, and polarized elementary electric-field modes. This representation allows one to propagate non-paraxial partially coherent vector fields using techniques for spatially fully coherent fields, which are numerically far more efficient than methods for propagating correlation functions. A procedure is given to determine the elementary modes from the radiant intensity and the far-zone polarization properties of the entire field. The method is applied to quasi-homogeneous fields with rotationally symmetric ${\text{cos}}^n\theta$ radiant intensity distributions (θ being the diffraction angle with respect to the optical axis and n being an integer). This is an adequate model for fields emitted by, e.g., many light-emitting diodes.