This paper proposes an efficient algorithm for tracking multiple targets using a network of static and mobile sensors (robots). Multi-target tracking has a broad array of applications, including crowd monitoring, vehicle tracking, warehouse automation, and pedestrian safety, among others. The problem of distributed labeled multi-target tracking comprises constraints on sensing range, communication, label consistency, and motion. Hence, our algorithm strives to minimize label mismatching, communication, movement of robots, and tracking error, which are serious concerns in the existing solutions. The problem is decomposed into two sub-problems: distributed estimation and adaptive movement control. We present a novel track consensus algorithm for estimating the number and tracks of targets, complemented by an efficient label consensus method. This algorithm can effectively identify similar tracks and fuse them in cluttered scenarios. Various movement control strategies are proposed to minimize the moving distance of the robots while keeping the maximum number of targets in the sensing range. The maximum target sensing problem is NP-hard; therefore, we propose and compare heuristic, approximation, and randomized algorithms. We have also verified our proposed solution through extensive simulations and compared the distributed estimation and movement control algorithms with other prominent solutions. We also analyze estimation accuracy using the Optimal Sub-Pattern Assignment (OSPA) metric, asymptotic performance, and communication cost and confirm the real-time computation of our proposed algorithms.