Controller and control method for internal combustion engine

A controller for an internal combustion engine is configured to control the internal combustion engine. The internal combustion engine includes an in-cylinder injection valve, an ignition device, an exhaust passage, and a three-way catalyst. The controller includes a fuel introduction processor configured to execute a fuel introduction process of introducing air-fuel mixture of fuel and air, which has been introduced into a cylinder, into the exhaust passage without burning the air-fuel mixture in the cylinder. The fuel introduction processor is configured to execute the fuel introduction process in a state in which only a port injection valve of the in-cylinder injection valve and the port injection valve performs fuel injection.