A fluid dispenser having a reservoir (1), a dispenser head (T) provided with a dispenser orifice (62), a dip tube (22), a pusher (6) axially movable over a determined stroke, an electric pump (4) that delivers air into the reservoir (1) so as to force the fluid through the dip tube (22) and actuated by the pusher (6), and a fluid outlet valve (7). All of the air coming from the electric pump is delivered into the reservoir. The electric pump (4) is activated by the pusher (6) as soon as it leaves its high rest position, and the outlet valve (7) is opened only in the proximity of the low depressed position, such that the electric pump (4) is electrically powered before the outlet valve (7) is opened and delivers air into the reservoir (1) with an increase in pressure that is less than 1 Bar.