Claudius reveals his internal conflict in this scene, discussing how his "stronger guilt defeats [his] strong intent" to pray (3.3.44). He knows that he has done something very wrong, but he realizes that there is no way in which he can truly be absolved or forgiven for his brother's murder, because he still retains the things for which he committed the murder: he wanted the crown, and he got it; he wanted his brother's wife, Gertrude, and he got her. He isn't willing to give these up. He knows that he cannot be "pardoned and retain th' offense" (3.3.60). He feels he has a "bosom black as death," but he tries to pray anyway. Hamlet actually has the chance to kill him right now, but the prince does not want to kill Claudius while he prays; rather, he wants to wait until a sinful moment so that Claudius will go straight to Hell, not having had a chance to seek absolution for his sins. Hamlet, of course, does not realize that Claudius's prayers are fruitless.
However, after Claudius's prayer, the king reiterates—alone on stage now that Hamlet has gone to his mother's room—that his words will not make it to heaven because his thoughts remain with those things here on earth. It's as though he feels guilty for the murder, but he doesn't really regret it, because he still wants the power and prestige and wife that it afforded him.