This paper introduces a new type of pseudopotentials, called Density Functional Semicore Pseudopotentials (DSPPs), designed for local orbital methods in density functional theory. The construction of these pseudopotentials is based on minimizing errors with norm conservation conditions for relevant ionic configurations of atoms from hydrogen to uranium. The DSPPs are optimized for two density functional approximations, the generalized gradient approximation (GGA) and the local density approximation (LDA), to ensure portability between different functionals. The paper explores the trade-offs between accuracy and portability, finding that the errors can be kept at a low level comparable to those for a single functional. The DSPPs are particularly useful for local orbital methods, allowing semicore functions to be treated as valence functions, which enhances accuracy and portability. A core density correction is also introduced to improve numerical stability and performance. The performance of DSPPs is evaluated through extensive test calculations for molecules and solids, showing that they perform well compared to all-electron calculations and other pseudopotential methods. The results suggest that the most significant approximation in these calculations remains the density functional approximation, while the DSPPs provide a more severe but manageable approximation.This paper introduces a new type of pseudopotentials, called Density Functional Semicore Pseudopotentials (DSPPs), designed for local orbital methods in density functional theory. The construction of these pseudopotentials is based on minimizing errors with norm conservation conditions for relevant ionic configurations of atoms from hydrogen to uranium. The DSPPs are optimized for two density functional approximations, the generalized gradient approximation (GGA) and the local density approximation (LDA), to ensure portability between different functionals. The paper explores the trade-offs between accuracy and portability, finding that the errors can be kept at a low level comparable to those for a single functional. The DSPPs are particularly useful for local orbital methods, allowing semicore functions to be treated as valence functions, which enhances accuracy and portability. A core density correction is also introduced to improve numerical stability and performance. The performance of DSPPs is evaluated through extensive test calculations for molecules and solids, showing that they perform well compared to all-electron calculations and other pseudopotential methods. The results suggest that the most significant approximation in these calculations remains the density functional approximation, while the DSPPs provide a more severe but manageable approximation.