In molecular dynamics (MD) simulations, calculations of potentials and their derivatives by coordinate, i.e., forces, in a pairwise additive manner such as the Lennard–Jones interactions and a short-range part of the Coulombic interactions form the main part of arithmetic operations. It is essential to achieve high thread-level parallelization efficiency of these pairwise additive calculations of potentials and forces to use current supercomputers with many-core architectures effectively. In this paper, we propose four new thread-level parallelization algorithms for the pairwise additive potential and force calculations. We implement the four codes in a MD calculation code based on the fast multipole method. Performance benchmarks were taken on the FX100 supercomputer and Intel Xeon Phi coprocessor. The code succeeds in achieving high thread-level parallelization efficiency with 32 threads on the FX100 and up to 60 threads on the Xeon Phi.