An integrated fuel combustion system with gas separation (adsorptive, absorptive, membrane or other suitable gas separation) separates a portion of carbon dioxide from a combustion gas mixture and provides for recycle of separated carbon dioxide to the intake of a fuel combustor for combustion. A process for carbon dioxide separation and recycle includes: admitting combustion gas to an adsorptive gas separation system contactor containing adsorbent material; adsorbing a portion of carbon dioxide; recovering a first product stream depleted in carbon dioxide for release or use; desorbing carbon dioxide from the adsorbent material and recovering a desorbed second product stream enriched in carbon dioxide for sequestration or use; admitting a conditioning and/or desorption fluid into the contactor and desorbing a second portion of carbon dioxide to recover a carbon dioxide enriched conditioning stream; and recycling a portion of the carbon dioxide enriched conditioning stream to an inlet of fuel combustor to pass through the fuel combustor for combustion.