A system for combusting carbon-containing fuel includes a reactor 10 for simultaneously supporting oxidation of the fuel and conversion of CO2 within the reactor. A metal oxide or metal is input to the reactor to convert the CO2 to a mineralized CO2 product. A cold trap 44 is provided for capturing exhaust gases from the reactor and returning condensate to the reactor, and a gas pump 50 maintains a desired vacuum or pressure within the reactor and the cold trap. Combustion products may be recycled to increase their energy value.