In order to provide a welded structure of and welding method for two metallic parts fitted together at a tubular section in a high-pressure fuel supply pump, an electric current is supplied to any of the welding connection surfaces formed between a pump housing and cylinder in a high-pressure fuel supply pump, between the pump housing and an installation flange, between the pump housing and an intake or discharge joint, between the pump housing and a pulsation-absorbing damper cover, between the pump housing and a relief valve mechanism, and between the pump housing and an electromagnetically driven intake valve mechanism. The two sections are pressed against each other to generate, along the connection surface, a plastic flow not causing melting or fusion due to heat, and form a diffusion-weld region at the connection surface by using the plastic flow and the application of the pressure.