Did you bench-bleed the new master cylinder? Have you checked for a leaking rear wheel cylinder?

Yes, I did bench-bleed the new master cylinder. It does not have rear wheel cylinders. It has master cylinder. Thanks.

Rear wheel cylinders refer to the rear brakes. It either has wheel cylinders with drum brakes or it has calipers with disc brakes. If you were not losing brake fluid, then your original master cylinder was most likely defective. You do not have to bleed all the way to the wheels when just replacing the master cylinder, but now that you have, there still could be air trapped in one of the lines. If you're already getting clear, new brake fluid at all the wheels, you may need to use a vacuum bleeder. That will pull the fluid out at the bleeder screw and will make air bubbles expand and come out easier.

Have you inspected the rear brakes? If a lining separates from the shoe frame and rotates a little, that will cause a low pedal.