An inkjet printer includes a printhead having first and second ports; an ink container for supplying ink to the printhead, the ink container having a supply port and a return port; a first ink conduit interconnecting the supply port and the first port; a second ink conduit interconnecting the return port and the second port; an ink valve positioned in the first ink conduit; a first pump positioned in the second conduit; and a second pump positioned in a valve bypass conduit. The first and second pumps are employed during pressurized priming of the printhead so as to optimize a pressure gradient along a length of the printhead.