It is true. Claudius reveals his uneasiness about Hamlet's actions in Act III.
After watching Hamlet's play, which included a scene in which the nephew of the king murdered his uncle, Claudius gets very angry and starts to suspect that Hamlet can be a threat to his power. In that way, in scene 3, Claudius calls Rosencratz and Guildenstern to give them an envelope that orders that Hamlet be taken to England. After they accept to do it, Claudius prays for his life and power since he is worried and also fears that Hamlet might kill him.