The special relativistic generalization of isotropic regularized kappa distributions is derived and compared to that of the original Olbertian (or standard) kappa distributions. It is demonstrated that for the latter, the kappa parameter is even more strongly limited than in the non-relativistic case, while for the former, all positive kappa values remain possible. After a derivation of non-relativistic limits, the pressures of the distributions are studied as a specific case of moments of both the relativistic standard and regularized kappa distributions.