We present a new algorithm that improves the prediction accuracy of the maximum charge and discharge power capabilities, i.e. state of power (SOP), of a battery state estimator (BSE) using an equivalent-circuit representation of a battery. For short time (high frequency) operation, lithium ion traction batteries are often dominated by ohmic and interfacial kinetic resistance, and conventional equivalent circuits employing resistors and capacitors (RC circuits) work well to characterize the system. However, for longer times, diffusion resistance becomes important and conventional BSEs based on RC elements fail to provide useful power predictions. In order to take into account diffusion in the SOP prediction, we propose to incorporate a nonlinear resistance into the power prediction formulas that are otherwise based on an RC circuit formulation; The diffusion effect is addressed with this nonlinear resistance whose value is proportional to the square root of time. The new approach is implemented in a vehicle-simulation environment (a hardware-in-the-loop setup) to predict the SOP of a lithium-ion battery. Simulation results demonstrate that this revised estimator provides much more accurate power prediction without compromising the regression performance of the original BSE.