System (10; 110) for controlling the closing of a door of a household appliance, in particular for a washing machine, such as a dishwasher; said door being adapted to close an inner chamber obtained in a cabinet of said household appliance and communicating with the outside environment through an access opening; said system (10; 110) comprising an engagement element mounted on said cabinet and adapted to be releasably held by a retaining element mounted on said door, so that said door is constrained to said cabinet when said household appliance is in use; wherein said engagement element comprises: - a supporting body adapted to be mounted on said cabinet; - a striker (14; 114) adapted to be releasably coupled to said retaining element and to be movably mounted relative to said supporting body between a retracted position and an extracted position; when said striker (14; 114) is coupled to said retaining element and assumes said retracted position and said extracted position, said door getting into a fully closed condition, in which it closes fluid-tight said access opening, and, respectively, a pre-open condition, in which it is spaced from said access opening in a manner such that it puts said inner chamber in fluidic communication with the environment outside said cabinet; - a locking mechanism, tending to switch from an unlocking condition, in which it is adapted to allow releasing said striker (14; 114), by allowing said striker (14; 114) to move from said retracted position to said extracted position when said striker (14; 114) is coupled to said retaining element, to a locking condition, in which it is adapted to allow holding said striker (14; 114) when said striker (14; 114) is in said retracted position; - electrically controlled actuator means adapted to control the switching of said locking mechanism from said locking condition to said unlocking condition; said system being characterized in that said engagement element further comprises - a thrust member (19; 119) capable of exerting a thrust in the direction of movement of said striker (14; 114) from said retracted position to said extracted position on said door, thereby facilitating the switching thereof into said pre-open condition when said striker is coupled to said retaining element and said locking mechanism is in the unlocking condition. - a supporting body adapted to be mounted on said cabinet; - a striker (14; 114) adapted to be releasably coupled to said retaining element and to be movably mounted relative to said supporting body between a retracted position and an extracted position; when said striker (14; 114) is coupled to said retaining element and assumes said retracted position and said extracted position, said door getting into a fully closed condition, in which it closes fluid-tight said access opening, and, respectively, a pre-open condition, in which it is spaced from said access opening in a manner such that it puts said inner chamber in fluidic communication with the environment outside said cabinet; - a locking mechanism, tending to switch from an unlocking condition, in which it is adapted to allow releasing said striker (14; 114), by allowing said striker (14; 114) to move from said retracted position to said extracted position when said striker (14; 114) is coupled to said retaining element, to a locking condition, in which it is adapted to allow holding said striker (14; 114) when said striker (14; 114) is in said retracted position; - electrically controlled actuator means adapted to control the switching of said locking mechanism from said locking condition to said unlocking condition; said system being characterized in that said engagement element further comprises - a thrust member (19; 119) capable of exerting a thrust in the direction of movement of said striker (14; 114) from said retracted position to said extracted position on said door, thereby facilitating the switching thereof into said pre-open condition when said striker is coupled to said retaining element and said locking mechanism is in the unlocking condition. - a locking mechanism, tending to switch from an unlocking condition, in which it is adapted to allow releasing said striker (14; 114), by allowing said striker (14; 114) to move from said retracted position to said extracted position when said striker (14; 114) is coupled to said retaining element, to a locking condition, in which it is adapted to allow holding said striker (14; 114) when said striker (14; 114) is in said retracted position; - electrically controlled actuator means adapted to control the switching of said locking mechanism from said locking condition to said unlocking condition; said system being characterized in that said engagement element further comprises - a thrust member (19; 119) capable of exerting a thrust in the direction of movement of said striker (14; 114) from said retracted position to said extracted position on said door, thereby facilitating the switching thereof into said pre-open condition when said striker is coupled to said retaining element and said locking mechanism is in the unlocking condition.