Robot systems for teleoperation commonly use a spring-like force pulling the follower robot towards the leader's position to track their movements. With this control strategy, the tracking accuracy deteriorates when the follower' stiffness is low, but high stiffness poses a danger to objects or people in the follower robot's environment. To address this trade-off between tracking accuracy and safety, we propose an alternative intention assimilation control (IAC) strategy where the robot's tracking accuracy can be ensured without high stiffness. Different from traditional approaches, which transmit the leader's current position to the follower, this new controller estimates the leader's target position and transmits it to the follower. With this strategy, the follower impedance can be changed on-the-fly to continuously reflect the user's desired impedance or modulated automatically to fulfill the task requirements. Our controller was validated on two 7 degree-of-freedom manipulators, yielding high tracking accuracy with varying impedance. Four experiments were conducted to compare {teleoperation} with IAC to tele-impedance control (TIC) during free tracking, interaction with a balloon, during peg insertion, and table polishing with force feedback. The results show that IAC increases tracking accuracy, improves task completion rate and reduces completion time. IAC enables the robot to accurately replicate the user's movement while giving them freedom to modulate the impedance according to their intention, providing an unprecedented level of control of the follower's position and its impedance during unilateral and bilateral teleoperation.