We report zero-field muon spin relaxation (mu SR) measurements on RFeAsO with R=La, Ce, Pr, and Sm. We study the interaction of the FeAs and R (rare-earth) electronic systems in the nonsuperconducting magnetically ordered parent compounds of RFeAsO(1-x)F(x) superconductors via a detailed comparison of the local hyperfine fields at the muon site with available Moumlssbauer spectroscopy and neutron-scattering data. These studies provide microscopic evidence of long-range commensurate magnetic Fe order with the Fe moments not varying by more than 15% within the series RFeAsO with R=La, Ce, Pr, and Sm. At low temperatures, long-range R magnetic order is also observed. Different combined Fe and R magnetic structures are proposed for all compounds using the muon site in the crystal structure obtained by electronic potential calculations. Our data point to a strong effect of R order on the iron subsystem in the case of different symmetry of Fe and R order parameters resulting in a Fe spin reorientation in the R-ordered phase in PrFeAsO. Our symmetry analysis proves the absence of collinear Fe-R Heisenberg interactions in RFeAsO. A strong Fe-Ce coupling due to non-Heisenberg anisotropic exchange is found in CeFeAsO which results in a large staggered Ce magnetization induced by the magnetically ordered Fe sublattice far above T(N)(Ce). Finally, we argue that the magnetic R-Fe interaction is probably not crucial for the observed enhanced superconductivity in RFeAsO(1-x)F(x) with a magnetic R ion.