A controller for an internal combustion engine includes a fuel introduction process of introducing an air-fuel mixture containing fuel injected by a fuel injection valve into an exhaust passage without burning the air-fuel mixture in a cylinder. The fuel introduction processor is configured to perform, during the execution of the fuel introduction process, a determination process of determining whether afterfire, in which the air-fuel mixture burns at an upstream side of a three-way catalyst device in the exhaust passage, has occurred and a stopping process of stopping the fuel introduction process when determining in the determination process that the afterfire has occurred.