Interfacial friction plays a crucial role in the mechanical properties of carbon nanotube based fibers, composites, and devices. Here we use molecular dynamics simulation to investigate the pressure effect on the friction within carbon nanotube bundles. It reveals that the intertube frictional force can be increased by a factor of 1.5-4, depending on tube chirality and radius, when all tubes collapse above a critical pressure and when the bundle remains collapsed with unloading down to atmospheric pressure. Furthermore, the overall cross-sectional area also decreases significantly for the collapsed structure, making the bundle stronger. Our study suggests a new and efficient way to reinforce nanotube fibers, possibly stronger than carbon fibers, for usage at ambient conditions.