The paper considers the influence of external forces on the behaviour of a redundant manipulator. It is assumed that the forces can act anywhere on the body of the manipulator. First, the equivalent generalized forces in the task space and the null space are defined and several special manipulator configurations regarding the equivalent forces and torques are identified. Next, two measures for the quantification of the influence of external forces on the task space are proposed. These measures are then used in the control algorithm to minimize the influence of external forces on the task space position accuracy. The control is based on the redundancy resolution at the acceleration level and the gradient projection technique. Improvement of the position accuracy is illustrated using the simulation of a four link planar manipulator.