It is understandable that he wanted Hamlet to move on quickly.
This speech seems carefully planned out, as if Claudius had written it out before he delivered it.
Claudius begins his speech saying, “’Tis sweet and commendable in your nature, Hamlet, To give these mourning duties to your father“, but that he “must know your father lost a father, That father lost, lost his.”(1.2.87-89) But he insults Hamlet, adding “’Tis unmanly grief.”(1.2.94) This is the opposite of what Claudius says to Laertes later in the play, where he says that he should act quickly, “Time qualifies the spark and fire of it. A kind of wick or snuff that will abate it”(4.7.114-116).
He would prefer it is Laertes acted while his feelings of hatred and revenge were still fresh, whereas it would be preferable if Hamlet be quiet about his father instead of keeping his memory fresh in everyone’s minds.
Instead of punishing Hamlet for Polonius’ murder himself, Claudius sent the prince to England alongside Rosencrantz and Guildenstern with letters that would arrange Hamlet’s death, making it look like an accident.
Despite the remorse shown in act 3 scene 3 when Claudius prays for forgiveness, he still wants Hamlet dead because he fears losing both his throne and his life.
The length of his speech to Hamlet also helps to obscure what he is saying, where as he is very clear and to the point with Laertes.
His speech was also more direct, intended only for Laertes, whereas his speech to Hamlet was also for Gertrude’s benefit.
After hearing about his father’s murder Hamlets sadness quickly turns into anger, and he plots the revenge that he feels his father deserves.
While this speech is given to Hamlet, it is for the benefit of Gertrude, who is instrumental in handling the emotional Hamlet.