An apparatus for controlling the operation of an internal combustion engine having a carburetor, especially, the air-fuel ratio and the rate of exhaust gas recirculation, controls the air-fuel ratio of the air-fuel mixture supplied to the engine in the steady operating condition of the engine on the basis of predetermined data determined relative to the engine crankshaft rotation speed and intake vacuum and stored previously in a memory. A three-way catalyst is used to purify engine exhaust gases, and an output signal from an O.sub.2 sensor in the exhaust system is fed back for the control of the air-fuel ratio in the engine exhaust gases. A circuit is provided to check whether this feedback control is normally carried or not. The air-fuel ratio of the air-fuel mixture supplied to the engine in an unsteady operating condition of the engine is controlled by regulating the amounts of fuel and air supplied to the engine while bypassing the carburetor, on the basis of the sensed values of the intake vacuum, engine crankshaft rotation speed and engine temperature and also depending on the throttle valve position. For the control of the rate of exhaust gas recirculation, an upper limit and a lower limit of the rate of opening of a recirculation rate regulating valve are determined on the basis of the sensed throttle valve opening, and other predetermined data determined relative to the engine crankshaft rotation speed and intake vacuum is read out from the memory to limit the rate of opening of the recirculation rate regulating valve.