In this paper we describe high-order multielectron ionization of large rare-gas clusters in strong laser fields in terms of initial ionization due to the suppression of electrostatic barriers and a subsequent dynamic ignition process in the Coulomb exploding cluster. The mechanism of a Xe-1100 cluster ionization in a strong laser field of 10(16) W/cm(2) is studied in a one-electron, one-dimensional approximation. The initial ionization is realized up to the total charge of Q(c) approximate to 1200, in the interval 2600 < Q(c) < 6600, where electrons are moving almost freely inside the cluster due to their high kinetic energy, the mechanisms of a direct energy enhancement are responsible for ionization. The Q(c) > 6600 ionization becomes possible when the cluster spatial expansion due to Coulomb explosion is taken into account.