A new density functional (DF) method is proposed for calculations of intermolecular interaction energies. The exchange-correlation functional was optimized in such a way that the method recovers the interaction energies with the dispersion (including exchange-dispersion) component subtracted and therefore our approach is named the dispersionless DF (dlDF) method. The dlDF method is shown to predict very well the dispersionless part of the interaction energy for all types of intermolecular interactions. Thus, if combined with a dispersion component, computed ab initio or from a simple function fitted to ab initio values, it provides accurate and physically justified interaction energies in the whole range of intermolecular separations. Our dispersion function is significantly more accurate than the published ones.