The invention relates to an instrument for robot-assisted minimally invasive surgery that offers increased dexterity at the distal end, where the active head of the surgical instrument, such as forceps, scissors, clip or dissector, is mounted. According to the invention, the instrument comprises an actuation module (3) provided with a mechanical interface (4) with five rotary elements (4a and 4b), a rod (5) with a flexible assembly (8) and a dexterity distal end (6) with three rotation couplings, the first and second couplings for orientation and rotation of the distal end (6) and the third one for moving the active surgical elements (22), where the distal end (6) has four movements which are controlled irrespective of the movement of the flexible assembly (8) and the orientation of said distal end (6) is achieved by means of some actuation wires (13b) passing through the bores of the elements of the flexible assembly (8) and the rotation of the distal end (6) is achieved by mechanical components that transmit the rotation from the rotary element (4a) of the actuation module (3) to the distal end (6), said mechanical component being located in the medial fibre of the rod (5) and the movements of the active surgical elements (22) being independent of the other movements and being achieved by means of some wires (13c and 13d) passing through the inside of the mechanical component that transmits the rotation from the rotary element (4a) to the distal end (6).