A fluid priming pump in combination with a reed valve for the control of incoming and exiting fluid flow is disclosed. The fluid priming pump includes a pump body and a movable plunger with the reed valve positioned adjacent the pump body. Two embodiments of the reed valve are disclosed, including an integral design where the unitary valve panel is insert molded with the valve body. In the second embodiment, the unitary reed valve is based on co-injection molding technology. Each reed valve design comprises only two component parts and becomes operable without the need for any additional mechanical components or fasteners. Pressure forces created by the fluid priming pump govern the opening and closing of valve panel portions for controlling the incoming and exiting fluid flow through the fluid priming pump.