The core-electron density in a molecule is defined as a sum of perfectly transferable, spherically symmetrical atomic contributions rho(AC)(Z,N,r). Analytical functions can be fitted to rho(AC)(Z,N,r) with a charge-conserving algorithm. The relativistic core-electron densities of the elements 3 through 118, obtained from numerical multiconfigurational Dirac-Fock calculations, are accurately represented by linear combinations of 50 s-type Gaussian primitives arranged in even-tempered basis sets. These representations are well suited for the augmentation of valence-electron densities produced by semiempirical methods and approaches involving effective core potentials. Calculations of the electronic properties of atoms in the TiCl4 and CdH2 molecules that employ such augmentation are presented.