This paper presents a system for improving the intuitiveness and responsiveness of assisted robot teleoperation interfaces by combining intent prediction and motion planning. Two technical contributions are described. First, an intent predictor estimates the user's desired task, and accepts freeform tasks that include both discrete types and continuous parameters (e.g., desired target positions). Second, a cooperative motion planner uses the task estimates to generate continuously updated robot trajectories by solving optimal control problems with timevarying objective functions. The planner is designed to respond interactively to changes in the indicated task, avoid collisions in cluttered environments, and achieve high-quality motions using a hybrid of numerical and sample-based techniques. The system is applied to the problem of controlling a 6D robot manipulator using 2D mouse input in the context of two tasks: static target reaching and dynamic trajectory tracking. Simulations suggest that it enables the robot to reach static targets faster and to track trajectories more closely than comparable techniques.