Recently, pre-trained state space models have shown great potential for video classification, which sequentially compresses visual tokens in videos with linear complexity, thereby improving the processing efficiency of video data while maintaining high performance. To apply powerful pre-trained models to downstream tasks, prompt learning is proposed to achieve efficient downstream task adaptation with only a small number of fine-tuned parameters. However, the sequentially compressed visual prompt tokens fail to capture the spatial and temporal contextual information in the video, thus limiting the effective propagation of spatial information within a video frame and temporal information between frames in the state compression model and the extraction of discriminative information. To tackle the above issue, we proposed a State Space Prompting (SSP) method for video understanding, which combines intra-frame and inter-frame prompts to aggregate and propagate key spatiotemporal information in the video. Specifically, an Intra-Frame Gathering (IFG) module is designed to aggregate spatial key information within each frame. Besides, an Inter-Frame Spreading (IFS) module is designed to spread discriminative spatio-temporal information across different frames. By adaptively balancing and compressing key spatio-temporal information within and between frames, our SSP effectively propagates discriminative information in videos in a complementary manner. Extensive experiments on four video benchmark datasets verify that our SSP significantly outperforms existing SOTA methods by 2.76% on average while reducing the overhead of fine-tuning parameters.