An aircraft propulsion assembly includes an engine, a nacelle surrounding the engine, and a system for extinguishing a fire that may occur in the engine and/or in the nacelle. The extinguishing system has means for supplying an extinguishant to at least one extinguishant distribution pipe which opens into a cavity of the engine and/or a cavity of the nacelle. The extinguishing system also includes means for supplying said at least one pipe with air so as to ventilate the or each cavity.