The Kharkov potential is a recent field theoretical model of the nucleon-nucleon (NN) interaction that has been built up in the framework of the instant form of relativistic dynamics starting with the total Hamiltonian of interacting meson and nucleon fields and using the method of unitary clothing transformations (UCTs). It is the first time that the relativistic UCT potential is used in the Faddeev equation to study nucleon-deuteron (Nd) elastic scattering. Our results of the relativistic Faddeev calculations with UCT describe elastic observables well up to 65 MeV, just like the corresponding nonrelativistic predictions. The theoretical predictions based on the Kharkov and CDBonn potentials are compared with recent precise experimental data ( iT11 , T20 , T21 and T22 ) taken at the deuteron beam of energy 186.6 MeV/nucleon.