The ink jet printer comprises a printhead (22) movable in front of a printing medium (30) and provided with an ink cartridge (25) integral with it; the cartridge is filled with ink from a main, high capacity tank (35), which is connected at intervals to the cartridge (25) by means of a capillary element. During each connection, the capillary element (101) is brought into contact with the sponge (41) inside the cartridge, while a peristaltic pump (134) mounted integral upon the main tank provides a pressure suitable for generating a sufficient flow of ink to refill the cartridge (25) in a short time frame. To perform the refilling, the cartridge is brought at the end of its stroke into a service station (5) mounted on the body of the main tank (35), which is moved against the cartridge by means of a motor-driven linkage, controlled by a refilling management program, in response to the signals of a cartridge ink level sensor.