A pump for dispensing a liquid contained in a bottle including a shrunk-fit section including an orifice for communicating with the liquid, a pushbutton including an orifice for ejecting the liquid, a dosing sleeve integrating a needle for plugging the ejection orifice and a device for bi-directional movement of the needle, a dosing piston including a channel equipped with a closing valve for the orifice, the piston being mounted in translation, in a leak-tight manner, inside the shrunk-fit section, between an open position and a closed position of the orifice, by means of the valve, an actuating member integral with the device for moving the needle and slidably mounted inside the dosing piston, by pressing on the pushbutton, the sliding assembly being set up to actuate the moving device and to position the valve in closed position so as to enable ejection of the liquid from the dosing chamber.