The device (1) has a rigid inserter (10) defining a through bore (12), and a pusher (30) driving an intrauterine device (2) with respect to the inserter. The pusher includes a distal end portion defining an elongated cavity opening on a free end edge (30A) of the distal end portion of the pusher, to coaxially receive an end (3.3) of a stem of the intrauterine device. The cavity defined by distal end portion of the push rod includes a flat bottom (34A) for bearing axially against another end (3.2) of the stem opposite to arms (4). An independent claim is also included for a medical kit.