Controller for internal combustion engine and method for controlling internal combustion engine

A controller for an internal combustion engine includes a processing circuit configured to execute a calculating process that calculates a returned air amount and an operating process that operates a fuel injection valve so that an air-fuel ratio of a mixture that is burned in a combustion chamber is controlled to a target value. The operating process includes under a condition in which the returned air amount is increased, having the fuel injection valve inject fuel increased in amount from a constant fuel amount, which is an amount of fuel injected when the returned air amount is unchanged, and under a condition in which the returned air amount is decreased, having the fuel injection valve inject fuel decreased in amount from the constant fuel amount.