We report parallel solutions of inverse multiple scattering problems with the Born iterative method (BIM) and the distorted Born iterative method (DBIM). The large computational costs of the Born solvers are reduced using the multilevel fast multipole algorithm (MLFMA). Furthermore, the solutions are obtained on supercomputing environments via parallelization of the Born solvers. This is achieved by two ways; the first way is to distribute independent scattering solutions within the Born iterations among parallel processes, and the latter is to parallelize MLFMA solver itself. We propose following both of the ways for efficient utilization of large computational resources. Parallelization of several scenarios are considered, including the cases where we have full-angle reconstruction at a single frequency and limited-angle reconstruction at multiple frequencies. These cases appear in typical applications of inverse scattering methods and results show that the parallelization scheme can obtain solutions with more than a thousand time speedup. This paper reports solutions involving medium-size scatterers on 128 computing nodes which are the largest-scale inversions so far according to our knowledge. Additional to the synthetic solutions, reconstruction of a real object with ultrasonic waves is demonstrated, along with pre-processing and calibration procedures of the measurement data.