A rotary piston engine comprises a housing having a trochoidal peripheral wall and side walls on both sides thereof, a rotor adapted to perform a planetary rotary motion along the inner surface of the peripheral wall, and intake and exhaust ports formed in the housing. The engine performs intake, compression, combustion and exhaust strokes of a working fluid in accordance with the planetary rotary motion of the rotor. An air injection port is formed in the peripheral wall of the housing between the exhaust port and a portion of the minor axis of the trochoidal curve, being adapted to communicate with the intake chamber formed between the peripheral wall and the rotor. Through the injection port, air and fuel are supplied into the housing to prevent recirculation of exhaust gas into the intake chamber of the engine, to stratify an air-fuel mixture of a richness appropriate for spark ignition and an air alone so as to facilitate the combustion of a lean air-fuel mixture as a whole, and to reduce harmful exhaust gases, particularly, hydrocarbon (HC) and carbon monoxide (CO) by the engine operation with the relatively lean air-fuel mixture.