Dynamical equations for a subsystem interacting with an environment are proposed which are adapted to a multiconfigurational form of the density operator. Initial correlations are accounted for in a non-Markovian master equation. Two variants of the latter are derived by projection operator techniques and cumulant expansion techniques, respectively. The present scheme is developed in view of describing the ultrafast dynamics in solute-solvent complexes where the details of system-environment correlations are of importance. The master equation is readily integrated into the equations of motion derived by the multiconfiguration time-dependent Hartree method, which provides an efficient scheme for the numerical propagation of the density operator.