Nonlinear interaction of a finite-amplitude electromagnetic wave with a uniform, unmagnetized plasma is considered, taking into account impurity-driven radiation losses. It is shown that this interaction is governed by the wave equation for electromagnetic sidebands, together with two coupled equations which are the electromagnetic radiation pressure-driven electron number density and temperature perturbations associated with plasma slow motions. The latter involve coupled radiative-Langmuir or ion-acoustic modes. Radiative thermal condensation instabilities are investigated in the absence of electromagnetic waves. The presence of an electromagnetic pump is shown to modify the spectra of radiative thermal condensation instabilities. This is demonstrated from the newly derived nonlinear dispersion relations. The relevance of the investigation to filamentary structures or jetting in laser-produced plasmas is pointed out.