We consider the challenges in estimating state-related changes in brain connectivity networks with a large number of nodes. Existing studies use sliding-window analysis or time-varying coefficient models which are unable to capture both smooth and abrupt changes simultaneously, and rely on ad-hoc approaches to the high-dimensional estimation. To overcome these limitations, we propose a Markov-switching dynamic factor model which allows the dynamic connectivity states in functional magnetic resonance imaging (fMRI) data to be driven by lower-dimensional latent factors. We specify a regime-switching vector autoregressive (SVAR) factor process to quantity the time-varying directed connectivity. The model enables a reliable, data-adaptive estimation of change-points of connectivity regimes and the massive dependencies associated with each regime. We develop a three-step estimation procedure: 1) extracting the factors using principal component analysis, 2) identifying connectivity regimes in a low-dimensional subspace based on the factor-based SVAR model, 3) constructing high-dimensional state connectivity metrics based on the subspace estimates. Simulation results show that our estimator outperforms K-means clustering of time-windowed coefficients, providing more accurate estimate of time-evolving connectivity. It achieves percentage of reduction in mean squared error by 60% when the network dimension is comparable to the sample size. When applied to resting-state fMRI data, our method successfully identifies modular organization in resting-state networks in consistency with other studies. It further reveals changes in brain states with variations across subjects and distinct large-scale directed connectivity patterns across states.