The effects of variations in gas pressure and discharge current on the properties of the ionization region in an argon magnetron sputtering discharge are investigated using a volume-averaged (global) model. The densities of thermal electrons, ions and metal atoms, the temperatures of both thermal and hot electron populations, the energies with which ions bombard the target, the sheath width adjacent to the cathode, as well as the ionized flux fraction are analyzed. Cu, Mo and Cu–Mo targets are considered. The studies are performed under conditions corresponding to experiments with a magnetron sputtering discharge (the neutral gas pressure ranges from 1.33 to 53.33 Pa and the discharge current from 50 to 300 mA). The results of the numerical calculations are used to explain the measured dependencies of the excitation temperature of argon atoms on discharge current determined by Boltzmann plot technique. The studies are conducted with the assumption that the energy distribution function for hot electrons is Maxwellian, as well as with the use of a more realistic model for hot electrons, which describes the energy distribution of these electrons using analytical expressions derived from the Boltzmann equation. In most cases, the calculated results agree well with the experimental data.