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In this paper, we present a higher-order multilevel fast multipole algorithm (MLFMA) for solving integral equations of electromagnetic wave scattering by three-dimensional conducting objects. We first employ higher-order parametric elements to provide an accurate modeling of the scatterer's geometry and then higher-order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. The resultant numerical system of equations is then solved using the MLFMA with a reduced computational complexity. Appropriate preconditioning techniques are employed to speedup the MLFMA solution.