Mechanism for moving a furniture door, apt to be placed on a lateral side of the piece of furniture and to move a door by a system of levers, the mechanism comprising a spring unit acting on the system of levers to balance the weight force of the door during opening, wherein the spring unit is pivotally mounted and acts directly on a main or thrust lever, mounted rotating around an axis, by a pin housed in a first cam slot formed in the lever and in a second cam slot placed in a fixed position with respect to the lateral side of the piece of furniture.