Identities for the electron intracule density I~R! in atoms and molecules are derived within the Hiller–Sucher–Feinberg ~HSF! formalism. It is proven that, when applied to arbitrary ~exact or approximate! electronic wave functions, these identities produce intracule densities that satisfy a modified condition for the electron coalescence cusp. A corollary of this proof provides a new, simplified derivation of the cusp condition for the exact I~R!. An expression for the Hartree–Fock approximation to the HSF electron intracule density that contains only twoand three-electron terms is obtained and its properties are analyzed. A simple scaling of the three-electron contributions in this expression assures integrability of the approximate I~R! and improves its overall accuracy. Numerical tests carried out for the H, He, Li, Be, Li, and Be systems demonstrate that the application of the scaled HSF-type identity to Hartree–Fock wave functions affords dramatic improvements in the short-range behavior of the electron intracule density. © 1995 American Institute of Physics.