"Oh Sato, nothing to forgive"
Dumb line for two reasons.
Sato spent the movie goading Miyagi into a fight to the death and sent his minions to harass and Daniel-san and his girlfriend. He arranged the physical assault on Daniel-san and his girlfriend and destruction of private property. He threatened to level the entire village including their church if Miyagi didn't agree to a death match.
Also consider that before he first left Okinawa, Miyagi was pitching woo with Sato's fiance.
So, this (in my humble opinion) is how that exchange should have gone:
Sato: "Forgive me, I beg you..."
Miyagi: "Only if you forgive me, my old friend"