OBJECTIVE Classification of electroencephalogram (EEG) signals obtained during motor imagery (MI) has substantial application potential, including for communication assistance and rehabilitation support for patients with motor impairments. These signals remain inherently susceptible to physiological artifacts (e.g., eye blinking, swallowing), which pose persistent challenges. Although Transformer-based approaches for classifying EEG signals have been widely adopted, they often struggle to capture fine-grained dependencies within them. APPROACH To overcome these limitations, we propose Cortical-SSM, a novel architecture that extends deep state space models to capture integrated dependencies of EEG signals across temporal, spatial, and frequency domains. We validated our method across two large-scale public MI EEG datasets containing more than 50 subjects. MAIN RESULTS Our method outperformed baseline methods on the two benchmarks. Furthermore, visual explanations derived from our model indicate that it effectively captures neurophysiologically relevant regions of EEG signals. Significance These results indicate that Cortical-SSM provides a robust and interpretable alternative to attention-based architectures for MI EEG decoding. By enabling physiologically grounded feature learning, our method advances the reliability of subject-independent EEG classification and supports the development of practical and clinically deployable brain-computer interface systems.