An exhaust manifold of an engine is connected to a three way (TW) catalyst, and the TW catalyst is connected to an NH.sub.3 adsorbing and oxidizing (NH.sub.3 -AO) catalyst, such as the Cu-zeolite catalyst. The engine performs the lean and the rich operations alternately and repeatedly. When the engine performs the rich operation, the TW catalyst synthesizes NH.sub.3 from NO.sub.x in the inflowing exhaust gas, and the NH.sub.3 is then adsorbed in the NH.sub.3 -AO catalyst. Next, when the engine performs the lean operation, NO.sub.x passes through the TW catalyst, and the adsorbed NH.sub.3 is desorbed and reduces the inflowing NO.sub.x. When the rich operation is in process, or is to be started, the exhaust gas temperature flowing into the NH.sub.3 -AO catalyst is detected. If the temperature is equal to or higher than the upper threshold representing the rich endurance temperature, the lean or the stoichiometric operation is performed.