A time-dependent density-functional theory (DFT) dynamics method in the electron nuclear dynamics (END) framework is presented. This time-dependent variational method treats simultaneously the nuclei and electrons of a system without utilizing predetermined potential energy surfaces. Like the simplest-level END, this method adopts a classical-mechanics description for the nuclei and a Thouless single-determinantal representation for the electrons. However, the electronic description is now expressed in a Kohn-Sham DFT form that provides electron correlation effects absent in the simplest-level END. Current implementation of this method employs the adiabatic approximation in the exchange-correlation action and potential. Simulations of molecular vibrations and proton-molecule reactions attest to the accuracy of the present method.