Despite its low-cost and broad material capability, material extrusion-based additive manufacturing suffers from low process resolution and dimensional accuracy, due to challenges with precisely controlling the ink flow rate during the printing process, particularly while using small nozzles and complex inks. In this paper, we present a novel approach to control the ink flow rate by utilizing (1) a printhead capable of concurrently monitoring and controlling the printing pressure (P) and steady-state flow rate (Q) and (2) an automatic iterative learning approach to elucidate the flow rate-pressure relationships for the system in the form of a Q-P relator model. Our studies showed that flow rate accuracy within 10% can be achieved with nozzles as small as 100 microns in diameter through implementation of the trained Q-P relator with both pressure and piston velocity-controlled printing. Particularly, Q-P relator enables proper selection of printing pressure to achieve desired flow rate during pressure-controlled printing, while providing a means of smart-priming of the system prior to velocity controlled printing to overcome the system transients. We also characterized the performance of the iterative learning process, focusing on time to convergence, effect of steady-state detection, and accuracy variation across various time scales. Presented results indicate that the proposed method will increase the microscale material extrusion process resolution and accuracy, and minimize material waste and reduce time to production.