Let \(E({\mathbb R}^n)\) be a rearrangement-invariant space and \(E'({\mathbb R}^n)\) be its associate space. Suppose a kernel \(G\) belongs to \(L_1({\mathbb R}^n)+E'({\mathbb R}^n)\). The space of potentials \(H_E^G({\mathbb R}^n)=\{u=G*f: f\in E({\mathbb R}^n)\}\) is studied. It is shown that this is a Banach space when equipped with the norm \(\|u\|_{H_E^G}=\inf\{\|f\|_E:f\in E({\mathbb R}^n), G*f=u\}\). Moreover, \(\|u\|_{E+L_\infty}\leq\|G\|_{L_1+E'}\|u\|_{H_E^G}\) for all \(u\in H_E^G\). The treatment covers spaces of classical Bessel and Riesz potentials. The main result of the paper is an equivalent characterization for the cone of the increasing rearrangements of potentials given under some conditions on \(G\).