Gene regulatory network (GRN)-based morphogenetic systems have recently attracted an increasing attention in artificial life and morphogenetic engineering research. However, the relationship between microscopic properties of intracellular GRNs and collective properties of morphogenetic systems has not been fully explored yet. Thus, we propose a new GRN-based framework to elucidate how critical dynamics of GRNs in individual cells affect cell fates such as proliferation, apoptosis, and differentiation in resulting morphogenetic systems. Our model represents an aggregation of cells, where each cell has a GRN in it. We used Kauffman's NK Boolean networks for GRNs. Specifically, we randomly assigned three cell fates to the attractors. Varying the properties of GRNs from ordered, through critical, to chaotic regimes, we observed the process that cells are aggregated. We found that the criticality of a GRN made an optimal partition of basins of attraction, which led to a maximum balance between cell fates. Based on the result, we can conclude that the criticality of a GRN is an important controller to determine the frequencies of cell fates in morphogenetic systems.