A rich-wait-time threshold value is set based on the NOx discharge amount per unit time discharged from an internal combustion engine. When the elapsed time, i.e. either the elapsed engine operation time since rich control was performed on a lean NOx trap catalyst device, or the elapsed engine operation time since the engine was started, becomes equal to or greater than the rich-wait-time threshold value, a determination that the rich control be started is added as a necessary condition for starting the rich control. Accordingly, an exhaust gas purification system for an internal combustion engine, an internal combustion engine, and an exhaust gas purification method for an internal combustion engine are provided, with which the execution timing of the rich control for recovering the NOx occlusion capacity of the lean NOx trap catalyst device is rendered more appropriate, and thus NOx reduction is performed with little fuel consumption deterioration.