A method is presented for the deposition of ultrathin superconducting NbNx films by atomic layer deposition enhanced by plasma from an organometallic precursor and an H-2/Ar gas mixture used as a reactant. The samples obtained are characterized by measurements of resistivity, spectral ellipsometry, atomic force microscopy, and measurements of superconducting characteristics. The optimal parameters of the H-2/Ar gas ratio are determined at which the resistivity of the NbNx films is minimal. A comparative analysis of the resistivity of the obtained NbNx films is carried out. The dependence of the temperature of transition to the superconducting state on film thickness is investigated. A transition temperature of 13.7 K and a critical current density of 0.7 MA/cm(2) are reached. The high film uniformity, precision control of the thickness, and deposition temperature of 350 degrees C make it possible to use these films in the production of field-effect transistors and in functional devices for various purposes, for example, in hot-electron bolometers, kinetic inductance detectors, and superconducting single-photon detectors.