Autonomous navigation n exploratory rovers requires mapping of the environment, localizing the rover in the map and path planning for collision free traversal from the current position of the rover to the goal state. Path planning algorithms fall into two broad categories: Reactive navigation and planned navigation algorithms. In this paper, we present a novel reactive navigation algorithm “Recursive Goal Seeking Algorithm (RGS)” for active window based exploration in autonomous rovers. The algorithm overcomes oscillatory behavior and dead traps associated with the existing potential fields based reactive navigation methods. RGS is based on recursive search of available paths through iterative positioning of sub-goal states along the path with minimum deviation from an asymptote obtained by joining the current position of the rover with the designated goal. We present the comparison between some of the traditional reactive navigation algorithms with the proposed one under different environment scenarios of varying obstacle distribution. The attractiveness of the proposed approach in overcoming the limitations of the existing algorithms is brought out through the results of extensive experiments. The algorithm has been validated on our experimental autonomous rover “Freelancer”.