A thread-milling cutter including a tool holder (2) and at least one cutting insert (3) with a longitudinal cutting edge (30) mounted on it. The tool holder (2) includes at least one pocket (20) extending essentially in an axial direction (A) and adapted for receiving the at least one insert (3). The cutting insert (3) has at least one positioning plane (31) on a first abutment surface of the insert (3) opposite the cutting edge (30) for a radial positioning of the insert (3) in the respective pocket (20). At least one protrusion (32) is provided on the abutment surface, a side surface (320) of the protrusion (32) being oriented at an angle (α) to the axial direction (A) of the cutter (1) and adapted for contacting a surface (22) of the pocket (20) for an axial positioning of the insert (3). Also described is an insert for a thread-milling cutter.