Eukaryotic genome stability is maintained by a complex and diverse set of molecular processes. One class of enzymes that promotes proper DNA repair, replication and cell cycle progression comprises small ubiquitin-like modifier (SUMO)-targeted E3 ligases, or STUbLs. Previously, we reported a role for the budding yeast STUbL synthetically lethal with sgs1 (Slx) 5/8 in preventing G2/M-phase arrest in a minichromosome maintenance protein 10 (Mcm10)-deficient model of replication stress. Here, we extend these studies to human cells, examining the requirement for the human STUbL RING finger protein 4 (RNF4) in MCM10 mutant cancer cells. We find that MCM10 and RNF4 independently promote origin firing but regulate DNA synthesis epistatically and, unlike in yeast, the negative genetic interaction between RNF4 and MCM10 causes cells to accumulate in G1-phase. When MCM10 is deficient, RNF4 prevents excessive DNA under-replication at hard-to-replicate regions that results in large DNA copy number alterations and severely reduced viability. Overall, our findings highlight that STUbLs participate in species-specific mechanisms to maintain genome stability, and that human RNF4 is required for origin activation in the presence of chronic replication stress.