This paper reports for the first time a computational analysis of the redox properties of graphene-supported Ru-porphyrins as potential catalytic materials for electrochemical CO₂ reduction. Density functional theory reveals that such catalytic ensembles can efficiently activate both CO₂ and CH₄ molecules indicating their generic utility as C₁-functionalization catalysts. The charge transfer from the graphene surface to the catalytic Ru centers influences the thermodynamic stability of the key reaction intermediates and therefore determines the selectivity of the electrochemical process. The electrochemical reduction of CO₂ can yield CO or methane, depending on the applied potential and reaction conditions. Calculations also identified alternative paths towards methanol and formic acid.