Understanding the uterine source of the electrophysiological activity of contractions during pregnancy is of scientific interest and potential clinical applications. In this work, we propose a method to estimate uterine source currents from magnetomyography (MMG) temporal course measurements on the abdominal surface. In particular, we develop a linear forward model, based on the quasistatic Maxwell's equations and a realistic four-compartment volume conductor, relating the magnetic fields to the source currents on the uterine surface through a lead-field matrix. To compute the lead-field matrix, we use a finite element method that considers the anisotropic property of the myometrium. We estimate the source currents by minimizing a constrained least-squares problem to solve the non-uniqueness issue of the inverse problem. Because we lack the ground truth of the source current, we propose to predict the intrauterine pressure from our estimated source currents by using an absolute-value-based method and compare the result with real abdominal deflection recorded during contractile activity. We test the feasibility of the lead-field matrix by displaying the lead fields that are generated by putative source currents at different locations in the myometrium: cervix and fundus, left and right, front and back. We then illustrate our method by using three synthetic MMG data sets, which are generated using our previously developed multiscale model of uterine contractions, and three real MMG data sets, one of which has simultaneous real abdominal deflection measurements. The numerical results demonstrate the ability of our method to capture the local contractile activity of human uterus during pregnancy. Moreover, the predicted intrauterine pressure is in fair agreement with the real abdominal deflection with respect to the timing of uterine contractions.