Even though Claudius might be justified in punishing Hamlet for Polonius's death, he knows that "the queen his mother / lives almost by [Hamlet's] looks" and that he has to consider "the great love the general gender bear [Hamlet]." If Claudius acts too hastily or with too little evidence, he risks the condemnation of his wife and his public. Instead, he uses Laertes's anger toward Hamlet to his own advantage. Claudius devises a plan "under the which [Hamlet] shall not choose but fall / And for his death no wind of blame shall breathe" toward himself. He tells Laertes that while he has been gone, Hamlet has had to endure talk of Laertes's accomplishments in dueling, and that this talk made Hamlet envious. Claudius plans to bait Hamlet into dueling with Laertes, but instead of using the customary dull rapier, Laertes will use "a sword unbated," that is, sharpened. As if that's not bad enough, Laertes says he will also "anoint [his] sword" with an "unction," or poison, so that if he so much as scratches Hamlet, he will surely die. And to top it all off, Claudius says that just in case Hamlet were to win the duel, he will have a poisoned drink prepared for the occasion.
Basically, Laertes is Claudius's fall-guy. Claudius sets Laertes up to be the one who gets the blame for killing Hamlet. Claudius still gets the end result he wants and receives none of the blame. But of course, the plan doesn't account for Hamlet's insight and intelligence and fails in the end.