In this paper, we propose a new spatio-temporal reconstruction scheme for the fast reconstruction of dynamic magnetic resonance imaging (dMRI) data from undersampled k-space measurements. To utilize both spatial and temporal redundancy in dMRI sequences, our method investigates the potential benefits of enforcing local spatial sparsity constraints on the difference to a reference image for each frame and additionally exploiting the low-rank property of global spatiotemporal signal via nuclear norm (NN) minimization. We present here an iterative algorithm that solves the convex optimization problem in an alternating fashion. The proposed method is tested on in-vivo 3D cardiac MRI and dynamic susceptibility contrast (DSC)-MRI brain perfusion datasets. In comparison to two state-of-the-art methods, numerical experiments demonstrate the superior performance of our method in terms of reconstruction accuracy.