The valve assembly (1) comprises a valve body (3-5) with an inlet port (6) and an outlet port (7) for the fluid, between which there is defined a main valve seat (9) intended to cooperate with an associated main obturator (10). The main obturator (10) defines together with the valve body (3-5), a variable volume control chamber (13) which is in permanent communication with the inlet port (6) through a first passage (11) having a reduced cross- section. The control chamber (13) is adapted to be brought into communication with the outlet port (7) through a second passage (24) having a larger cross-section. The valve assembly (1) also comprises a solenoid pilot valve (17) including a control coil (18) and a movable core (19) associated with an auxiliary obturator (21) which is adapted to open and close the second passage (24). In the valve body (3-5), between the second passage (24) and the outlet port (7), there is defined a second variable volume control chamber (22), which is delimited in part by the auxiliary obturator (21), and the movable core (19) associated with the auxiliary obturator (21) is mounted outside of the flow-path of the fluid, in particular outside of the second variable- volume control chamber (22).