Stable plasma ignition of remote plasma sources (RPSs) for various plasma processes is essential to ensure the stability of the discharge, steady operating conditions, and high plasma density. In an RPS in which the gas pressure exceeds 1 Torr, the reaction paths leading to the high-level excited state play an essential role in the power balance and energy cascade at high applied input power. In this study, 97 chemical reactions in a detailed reaction set involving argon discharge are investigated in the steady-state to understand the extent to which the dominant reactions are affected by variations in the process parameters. We observed that the stepwise ionization process of the argon 4p excited state significantly contributes to sustaining high-density plasmas in the near 1 Torr regime.