With the majority of mobile robot path planning methods being focused on obstacle avoidance, this paper, studies the problem of Navigation Among Movable Obstacles (NAMO) in an unknown environment, with static (i.e., that cannot be moved by a robot) and movable (i.e., that can be moved by a robot) objects. In particular, we focus on a specific instance of the NAMO problem in which the obstacles have to be moved to predefined storage zones. To tackle this problem, we propose an online planning algorithm that allows the robot to reach the desired goal position while detecting movable objects with the objective to push them towards storage zones to shorten the planned path. Moreover, we tackle the challenging problem where an obstacle might block the movability of another one, and thus, a combined displacement plan needs to be applied. To demonstrate the new algorithm's correctness and efficiency, we report experimental results on various challenging path planning scenarios. The presented method has significantly better time performance than the baseline, while also introducing multiple novel functionalities for the NAMO problem.INDEX TERMS Motion and path planning, navigation among movable obstacles, mobile robots.