  Let $M$ be a domain enclosed between two principal orbits on a cohomogeneity
one manifold $M_1$. Suppose $T$ and $R$ are symmetric invariant (0,2)-tensor
fields on $M$ and $\partial M$, respectively. The paper studies the prescribed
Ricci curvature equation $\mathrm{Ric}(G)=T$ for a Riemannian metric $G$ on $M$
subject to the boundary condition $G_{\partial M}=R$ (the notation $G_{\partial
M}$ here stands for the metric induced by $G$ on $\partial M$). Imposing a
standard assumption on $M_1$, we describe a set of requirements on $T$ and $R$
that guarantee global and local solvability.
