A system (10, 110) includes an engagement element (11) mounted on a household appliance (W) door (D). A supporting body (12) is releasably held by a retaining element (16) mounted on a cabinet (C). A striker (14, 114) releasably couples to the retaining element (16) and moves between retracted and extracted positions. When the striker (14; 114) is retracted the door (D) is fully closed, and when extracted the door is pre-opened relative to the cabinet (C). An actuator (20) controls a locking mechanism (18) that tends to switch from an unlocked condition, allowing the striker (14,114) to move from the retracted to the extracted position, to a locked condition, holding the striker (14, 114) in the retracted position. A thrust member (19, 119) exerts thrust on the door (D), facilitating switching to pre-opened when the striker (14) couples to the retaining element (16), locking the locking mechanism (18).