In Act V, Hamlet asks for Laertes forgiveness. He says he knows he has done Laertes wrong by killing Polonius but Hamlet claims he has an illness which causes him madness as times. His exact words are:
"Give me your pardon, sir. I have done you wrong;
But pardon't, as you are a gentleman.
This presence knows,
And you must needs have heard, how I am punish'd
With sore distraction. What I have done
That might your nature, honour, and exception
Roughly awake, I here proclaim was madness.( V,ii,217-223)
Laertes grudgingly accepts the apology but says he will also wait for an official inquiry into the death of his father. He says,
"I am satisfied in nature,
Whose motive in this case should stir me most
To my revenge. But in my terms of honour
I stand aloof,. . ."
Then the sword fight between Laertes and Hamlet begins. As the fight progresses, Laertes realizes he has been wrong about Hamlet, and as he is dying he asks Hamlet "to exchange forgiveness with him."