The impact of large exhaust gas dilution (up to 59.5% H2O and 30.3% CO2 per vol.) on the heterogeneous (catalytic) and homogeneous (gas-phase) steady combustion of fuel-lean CH4O2N2 mixtures over platinum has been investigated experimentally and numerically at pressures of 5 to 14 bar. In situ, one-dimensional Raman measurements of major gas-phase species concentrations and planar laser induced fluorescence (LIF) of the OH radical were used to assess the heterogeneous and homogeneous combustion processes, respectively. Comparisons between measurements and predictions have yielded catalytic and gas-phase chemical reaction schemes suitable for the combustion of methane with large H2O and CO2 dilution. The addition of water inhibits the catalytic reactivity due to the increase in the surface coverage of OH(s) that, in turn, reduces the available free platinum sites. This inhibition has been quantified in terms of operating pressure, temperature, and amount of water dilution through an appropriate one-step catalytic reaction for the complete oxidation of methane. Water promotes chemically the onset of homogeneous ignition, as it directly impacts the radical pool buildup. On the other hand, the chemical effect of CO2 on either reaction pathway is negligible. The influence of H2O and CO2 dilution to the coupling between the two reaction pathways is elucidated and implications for the application of catalytically stabilized combustion to new power generation cycles with large exhaust gas dilution are addressed.