The inventions relate to means for purifying water, primarily drinking water, and can be used in domestic water purification systems. The claimed filtered water storage unit for the storage device of a water purification system comprises a housing, an elastic chamber disposed therein for filtered water, and a region for pressurizing untreated water, which is defined between the wall of the chamber and the wall of the housing. The elastic chamber is made of a modified biaxially oriented thermoplastic elastomer and consists of a chamber body and neck, formed as a single piece, the neck being rigidly secured in the housing. The water purification system comprises a reverse osmosis membrane, a clean water discharge pipe, an overflow into a drain, a clean water tap, and a storage device comprising a filtered water storage unit and a hydroautomatic unit. In a first embodiment of a system with a storage device, the outlet of the controlled chamber of a valve for controlling pressurization of the water is associated with the water pressurizing region in the housing of the water storage unit, and the input of the controlling chamber of a valve for controlling drainage is associated with the clean water discharge pipe upstream of the tap, wherein the valve for controlling pressurization of the water is normally open and the valve for controlling drainage is normally closed. The claimed water purification system is highly reliable and provides a high quality of purified water.