Stoppable flushing mechanism having an assured minimum flow of water is provided with an evacuation orifice having a sealing edge adapted to be positioned in a base of a flushing tank, and a substantially axially movable valve capable of being applied to the sealing edge. A substantially axially movable floater is affixed to the valve and adapted to maintain the valve at a distance from the sealing edge during evacuation of water. A transmission and lifting system is provided for moving the valve, and a push-button control device activates the transmission and lifting system. The transmission and lifting system includes a buoyancy chamber having a first base, with the buoyancy chamber being arranged in an upper portion of a housing in which the floater is housed and being associated with a rapid evacuation mechanism comprising at least one element activatable by the push-button control device, and at least one orifice in the first base or in a vicinity of the first base of the buoyancy chamber. The rapid evacuation mechanism is placed in an operative position when the push-button control device is pressed and in an inoperative position when the push-button control device is no longer pressed.