A method and system for steam generation and purification is presented. The method includes receiving a fuel stream, a water stream, and an oxidant stream in a direct contact steam generation (DCSG) apparatus; and generating a gas mixture stream comprising steam and carbon dioxide (CO2) in the DCSG apparatus. The method further includes receiving at least a portion of the gas mixture stream in a membrane separator, and separating at least a portion of the steam from the gas mixture stream to generate a permeate stream. The method further includes recirculating at least a portion of the permeate stream to the DCSG apparatus; monitoring a CO2 content in the gas mixture stream; and discharging at least a portion of the gas mixture stream at an outlet of the DCSG apparatus as a product stream if the CO2 content is lower than a determined value.