Controller and control method for internal combustion engine

A controller for an internal combustion engine mounted on a vehicle, wherein the internal combustion engine includes an exhaust purification device configured to purify exhaust gas discharged from a plurality of cylinders and a plurality of fuel injection valves provided for the respective cylinders, the controller comprising processing circuitry configured to execute

• a dither control process of operating the fuel injection valves to designate at least one of the cylinders as a lean combustion cylinder, in which an air-fuel ratio is leaner than a stoichiometric air-fuel ratio, and to designate at least another one of the cylinders as a rich combustion cylinder, in which an air-fuel ratio is richer than the stoichiometric air-fuel ratio, and
• an idle-time limiting process of causing an absolute value of a difference between the air-fuel ratio in the lean combustion cylinder and the air-fuel ratio in the rich combustion cylinder to be smaller when the internal combustion engine is idling than when the internal combustion engine is not idling.