The pre-mix burner assembly includes a jet pump comprising a suction chamber, a flue gas inlet, and a combustion air tube with a combustion air nozzle. The combustion air inlet includes a combustion air tube with a tapered nozzle, and it is connected to a combustion air fan. The flue gas inlet is connected to the suction chamber and the combustion air fan. The suction chamber surrounds the combustion air tube, and it has a jet pump nozzle with a discharge. The assembly includes a fuel gas inlet connected to the combustion air tube. The combustion air and fuel gas mixture exits the combustion air nozzle creating a negative pressure in the suction chamber and drawing flue gas into the suction chamber. The assembly includes a mixing tube positioned downstream of the jet pump discharge, and a burner block connected to an outlet of the mixing tube.