An apparatus for transferring a specimen container from a departure support to a container which includes a gripper supporting frame and a container gripper selectively movable with respect to the frame between an upper position and lower position in which gripper fingers of the container gripper are able to catch a container in a departure support or to leave the container in a container carrier. The apparatus further includes a gripper blocking element movable between a work position, in which said gripper blocking element stops the movement of the container gripper towards the lower position in an intermediate position between the upper and lower positions, and a rest position in which the gripper blocking element allows the container gripper to reach the lower position sliding along the lateral surface of the container.