A door latch for retaining a door to a door frame or floor at a plurality of locations adjacent a respective edge of the door includes a central latch disposed within the door and biased in an extended position, and at least one of an upper latch disposed within the door and biased in an extended position and a lower latch disposed within the door and biased in an extended position. The door latch further includes a lock set that is operable for simultaneously moving the central latch and the at least one of the upper latch and the lower latch from the extended position to a retracted position so as to release the door from the door frame. The door latch includes a rotatable central shaft operably coupled with a cam, and a connecting arm operably coupled with the cam and attached to an actuator rod. The actuator rod is connected to an inner sleeve moveably disposed within an outer housing of the upper latch or the lower latch. Movement of the actuator rod creates a tension force that is greater than the biasing force exerted on the inner sleeve to move the inner sleeve from the extended position to the retracted position.