Propagation-based phase-contrast tomography has become a valuable tool for visualization of three-dimensional biological samples, due to its high sensitivity and its potential in providing increased contrast between materials with similar absorption properties. We present a statistical iterative reconstruction algorithm for this imaging technique in the near-field regime. Under the assumption of a single material, the propagation of the x-ray wavefield-relying on the transport-of-intensity equation-is made an integral part of the tomographic reconstruction problem. With a statistical approach acting directly on the measured intensities, we find an unconstrained nonlinear optimization formulation whose solution yields the three-dimensional distribution of the sample. This formulation not only omits the intermediate step of retrieving the projected thicknesses but also takes the statistical properties of the measurements into account and incorporates prior knowledge about the sample in the form of regularization techniques. We show some advantages of this integrated approach compared to two-step approaches on data obtained using a commercially available x-ray micro-tomography system. In particular, we address one of the most considerable challenges of the imaging technique, namely, the artifacts arising from samples containing highly absorbing features. With the use of statistical weights in our noise model, we can account for these materials and recover features in the vicinity of the highly absorbing features that are lost in the conventional two-step approaches. In addition, the statistical modeling of our reconstruction approach will prove particularly beneficial in the ongoing transition of this imaging technique from synchrotron facilities to laboratory setups.