An axially adjustable tool holder, having a principal body (1)with attachment, in a recess (2) of which is slidably mounted a mobile part (3) for mounting a tool (4). The mobile part (3) cooperates with a ring for transverse adjustment (5), mounted in rotation on the extremity of the principal body (1)with the recess (2) and secured transversely to said extremity, by a ball bearing device (8), in the form of a sleeve with an interior thread (5′). The ball bearing device (8) presenting axial play of the ring for transverse adjustment (5), when the mobile part (3) is tightened, application of the proximal face (51) of the adjustment ring (5)against a corresponding distal external supporting flange (1′) of the principal body (1). The mobile part (3) being locked in working position, after adjustment, by a device for tightening (6) by traction cooperating with a part (7) of the mobile part (3).