The present invention relates to a dispensing system intended to be secured to a container in which a fluid product is packaged, said dispensing system comprising a pump (1), an inlet non-return valve and an outlet non-return valve, an elastic return means (4) and a push button (3), said pump (1) being set in motion by way of a pushing action on the push button (3) connected to said pump (1). The dispensing system according to the invention is characterized in that it is made up of three one-piece structural parts: a rod (5), a collar (2) and the push button (3), at least one flap (6, 7) has a flexible and deformable peripheral region (70, 80) that is not perforated and is situated opposite the rigid support (24, 52).