In the present work, the hybrid cellular automaton model of the initial stages of aggregation of the cellular slime mold Dictyostelium discoideum, proposed by the authors earlier, is modified by taking into account the dependence of myxamoebae movement on the intracellular Ca2+ concentration. The cellular automaton is a three-dimensional grid the cells of which are either empty or contain one amoeba, the state of the automaton being determined by the distribution of amoebae over the grid. At each time step, the state of the automaton changes according to fixed rules which are determined by solutions to systems of equations that describe the distribution of aggregation factors in the medium and their concentrations inside cells. Movements of amoebae can be either directed along the concentration gradient of cyclic adenosine monophosphate, or random walk. The calculation results show that when the aggregate reaches a certain size its growth stops and the number of cells in it fluctuates around the average value. Such behavior suggests that aggregation is determined by two competing mechanisms: one promotes the growth of the aggregate while the other promotes detachment of cells or small clusters from it.