Abstract: An interatomic potential model that can simultaneously describe metallic, covalent, and ionic bonding is suggested by combining the second nearest-neighbor modified embedded-atom method (2NNMEAM) and the charge equilibration (Qeq) method, as a further improvement of a series of existing models. Paying special attention to the removal of known problems found in the original Qeq model, a mathematical form for the atomic energy is newly developed, and carefully selected computational techniques are adapted for energy minimization, summation of Coulomb interaction, and charge representation. The model is applied to the Ti-O and Si-O binary systems selected as representative oxide systems for a metallic element and a covalent element. The reliability of the present 2NNMEAM+Qeq potential is evaluated by calculating the fundamental physical properties of a wide range of titanium and silicon oxides and comparing them with experimental data, density functional theory calculations, and other calculations based on (semi-)empirical potential models.