The local pseudopotential (LPP) is an important component of orbital-free density functional theory, a promising large-scale simulation method that can maintain information on a material's electron state. The LPP is usually extracted from solid-state density functional theory calculations, thereby it is difficult to assess its transferability to cases involving very different chemical environments. Here, we reveal a fundamental relation between the first-principles norm-conserving pseudopotential (NCPP) and the LPP. On the basis of this relationship, we demonstrate that the LPP can be constructed optimally from the NCPP for a large number of elements using the optimized effective potential method. Specially, our method provides a unified scheme for constructing and assessing the LPP within the framework of first-principles pseudopotentials. Our practice reveals that the existence of a valid LPP with high transferability may strongly depend on the element.