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Neural circuits produce signals that are complex and nonlinear. To facilitate the understanding of neural dynamics, a popular approach is to fit state space models (SSM) to the data and analyze the dynamics of the low-dimensional latent variables. Despite the power of SSM to explain the dynamics of neural circuits, these models have been shown to merely capture statistical associations in the data and cannot be causally interpreted. Therefore, an important research problem is to build models that can predict neural dynamics under causal manipulations. Here, we propose interventional state-space models (iSSM), a class of causal models that can predict neural responses to novel perturbations. We draw on recent advances in causal dynamical systems and present theoretical results for the identifiability of iSSM. In simulations of the motor cortex, we show that iSSM can recover the true latents and the underlying dynamics. In addition, we illustrate two applications of iSSM in biological datasets. First, we applied iSSM to a dataset of calcium recordings from ALM neurons in mice during photostimulation. Second, we applied iSSM to a dataset of electrophysiological recordings from macaque dlPFC during micro-stimulation. In both cases, we show that iSSM outperforms SSM and results in identifiable parameters. The code is available at https://github.com/amin-nejat/issm.