"He says that he loves you."
Translation:Říká, že tě miluje.
"Říká, že miluje tebe" stresses the "you" so a good way to translate that to English would be "He says it's you that he loves," or in speech you could say "He says he loves YOU!"
"Říká, že tě miluje" puts more emphasis on the "love" part - this is the main new information the speaker presents. "He says he loves you (maybe you thought he didn't)"
Also note that "říkat" has a long í (although the form with short i exists in some dialects).