"He does not mean it like that" should be an allowed translation.
However, I am not quite certain about "He does not mean it", and I think it should be accepted too. Imagine person A saying to person B: "You're just annoying." A typical German phrase to calm person B would be "Er meint es nicht so." In English you would probably say: "He doesn't mean it".
He is not serious ???? Not a literal translation, but more intentional.
Someone says: "He should burn in hell" and then somebody else wants to calm it down. What do they say in Washington then: "He does not mean it." ???? I don't think so. More something like: He is not serious, don't listen to him, he is drunk.