Admittance control can improve robot performance and robustness in interactive tasks, but is still limited by stability when implemented on low-admittance hardware, such as position-controlled industrial robots. This limits applications which require the payload, reach, or positioning accuracy. While the idealized reference admittance behavior would be stable with any passive environment (provided positive damping), real robots can be unstable, especially with high-stiffness environments. Thus, instability comes from deviation from the ideal reference model, due to either inner-loop bandwidth, time-delay, or other model error. To improve accuracy of rendered dynamics and reduce contact forces, a novel integrated disturbance observer-based admittance control method which is implemented on a position/velocity-controlled industrial robot in task space is proposed. The multisensor information, i.e., the velocity command, measured output velocity, inverse model of the velocity controlled system, and the force/torque (F/T) sensor measurement are integrated to estimate and cancel the disturbances, outside the position/velocity control loop, all in task space. Theoretical analyses and experiments on the actual robot show that the proposed method is able to improve accuracy and reduce contact forces even at higher admittance.