The performance of an updated time-domain least-squares identification method for identifying a reduced-order linear system model in case of limited response measurements and its use in structural health monitoring is evaluated. It is shown that the incorporation of a mass-invariability constraint enhances the robustness of the parametric identification procedure. The full structural stiffness and mass matrices are identified from the identified reduced-order model by using the condensed model identification and recovery method. The damage state is considered to be represented by an incremental stiffness degradation model. The degradation in stiffness is estimated through the minimization of an error function defined in terms of Rayleigh quotients. The performance of the proposed scheme is examined with reference to the simulated damage due to earthquake excitation in a 10-story building with rigid floor diaphragm.