The high-pressure pump (7) comprises a number of pumping elements (18) actuated in reciprocating motion through corresponding suction and delivery strokes. Each pumping element (18) is provided with a corresponding intake valve (25) in communication with an intake pipe (10) supplied by a low-pressure pump (9). Set on the intake pipe (10) is an on-off solenoid valve (27) having a reduced flow rate substantially of the same order of magnitude as the maximum amount of fuel that can be injected by an injector (5). The solenoid valve (27) is controlled in a chopped way in synchronism with an intermediate part (32) of the suction stroke of each pumping element (18).