In a machine for extracorporeal blood treatment, a syringe pump (4) for infusion of an anticoagulant comprises a support (5) for the syringe, a pusher (6), a sensor of the pushing force of the pusher (6), and a control unit (8) for guiding the pusher (6) in accordance with the force measured by the sensor. The support comprises a series of interchangeable gripping elements (9), each of which defines a housing for a syringe having a different diameter, the housing having a longitudinal axis which, for all of the interchangeable gripping elements in the series, is always in the same position in relation to the pusher. The invention provides a dialysis machine with a pump that is easily and rapidly adaptable for syringes over a wide range of sizes.