The objective of the present work is to characterize, in the multiparameter case, priors ensuring, up to \(o(n^{-1})\), the frequentist validity of confidence regions based on the highest posterior density (HPD). In the Bayesian context, the use of such regions is particularly appealing. The present problem was studied earlier in the one-parameter case by \textit{H. W. Peers} [J. R. Stat. Soc., Ser. B30, 535-544 (1968)] who considered posterior regions in the form of intervals with equal posterior densities at the extremeties. The approach of Peers does not seem to work in the multiparameter case and new techniques are called for. This has been attempted in the next section. We have also investigated conditions under which the HPD regions based on Jeffreys' prior have frequentist validity up to \(o(n^{-1})\).