Why didn't you punish Hamlet yet, for your own safety and justice?
I did it for my wife and the kingdom, who love him.
My noble father is now dead. And my sister has gone mad. I must have my revenge!
I love your father and I love myself. I have plans. Soon...
As you should, will you allow me to help you?
I can't wait to see him when I tell him that he did this.
I'm coming back, and I can't wait to look into your 'kingly eyes'.
Claudius explains that he didn't take immediate action against Hamlet because both the queen (who he loves dearly) and the public (who would punish King Claudius) love Hamlet.
Claudius is explaining that he wants revenge on Hamlet just as bad as Laertes does. Laertes is in pain due to the death of his father and his sister going mad, both due to Hamlet.
A messenger delivers messages to the King and Queen. They are from Hamlet, which makes Laertes want revenge even more. Claudius asks if he can lead Laertes and Laertes agrees, as long as the king does not lead him to peace.