Abstract: Robots interacting with humans must be safe, reactive and adapt online to unforeseen environmental and task changes. Achieving these requirements concurrently is a challenge as interactive planners lack formal safety guarantees, while safe motion planners lack flexibility to adapt. To tackle this, we propose a modular control architecture that generates both safe and reactive motion plans for human-robot interaction by integrating temporal logic-based discrete task level plans with continuous dynamical system (DS)-based motion plans. We formulate a reactive temporal logic formula that enables users to define task specifications through structured language, and propose a planning algorithm at the task level that generates a sequence of desired robot behaviors while being adaptive to environmental changes. At the motion level, we incorporate control Lyapunov functions and control barrier functions to compute stable and safe DS-based motion plans online at 1~KHz that focus on two types of robot behaviors: (i) complex, possibly periodic motions given by an autonomous DS, and (ii) time-critical tasks specified by Signal Temporal Logic~(STL). Our methodology is demonstrated on the Franka robot arm performing wiping tasks on a whiteboard and a human mannequin that is compliant with human interactions and dynamically adapts to environmental changes.