The influence of the kinetics of excited atoms on the characteristics of an inductively coupled plasma in argon during the early afterglow is studied. A self-consistent model including the nonlocal approach for the kinetic treatment of the electrons is applied. Parameters of both the steady state of the rf discharge and the decay phase are presented. Results for the steady-state densities of excited atoms as well as temporal evolutions of the wall potential and mean energy of electrons are discussed in comparison with experimental data available from the literature. The ionization kinetics of the electrons, the electron power balance, and the main kinetic pathways for excited argon atoms are analyzed in the pressure range between 0.5 and 133 Pa . In particular, a significant influence of the excited atoms on the plasma behavior in steady state and during the afterglow is found.