The hadronization procedure of the QGSJET-III Monte Carlo (MC) generator of high energy hadronic interactions is discussed. Selected results of the model, regarding production spectra of secondary particles, are presented in comparison to experimental data and to the corresponding predictions of the QGSJET-II-04 MC generator. The model is applied to calculations of basic characteristics of extensive air showers initiated by cosmic ray interactions in the atmosphere and the results are compared to predictions of other MC generators of cosmic ray interactions.