A method for manufacturing an integral rotationally symmetrical part, which includes producing a blank of the part around a cylindrical mandrel, the blank including at least one fibrous structure made of composite ceramic fibers coated with metal, followed by a diffusion-welding treatment of the blank by hot isostatic pressing, and optionally machining the thus-treated blank to obtain the part. The blank includes at least a first metal-wire layer between the mandrel and the composite fibrous structure, and at least a second metal-wire layer arranged around the composite fibrous structure to cover the composite fibrous structure.