Vegetation, wildfire and atmospheric oxygen on Earth have changed throughout geological times, and are dependent on each other, determining the evolution of ecosystems, the carbon cycle, and the climate, as found in the fossil record. Previous work in the literature has only studied flaming wildfires, but smouldering is the most persistent type of fire phenomena, consuming large amounts of biomass. In this study, the dependence of smouldering fires in peatlands, the largest wildfires on Earth, with atmospheric oxygen is investigated. A physics-based computational model of reactive porous media is developed which was previously validated against experiments. Simulations are conducted for wide ranges of atmospheric oxygen concentrations and fuel moisture contents to find thresholds for ignition and extinction. Results show that the predicted rate of spread increases in oxygen-rich atmospheres, while it decreases over wetter fuels. A novel nonlinear relationship between critical oxygen and critical moisture is found. More importantly, we show that compared to previous work on flaming fires, smouldering fires can be ignited and sustained at a substantially higher moisture content (> 100%), and at a substantially lower oxygen concentration (∼ 12%). This defines a possible lower oxygen threshold for wildfire and could help interpret the char remains and paleo fire activities seen in the fossil record.