Misunderstanding is often used as a euphemism for disagreement, or even fight.
It sounds here that you thought your friend meant something to which you took exception. If you mow believe that your friend may have meant something different, but you misunderstood him, then you can say:
I apologise, I thought you were saying X, and that upset me, but now I realise you only meant Y
If you still think your friend meant what you thought he meant, then it would not be true to say there was a misunderstanding.
It is not really possible to apologise for misunderstanding your friend, and than ask him for clarification. That implies you don't feel confident there has been a misunderstanding at all.
You can say
I am very sorry about the argument. I misunderstood you. I thought you were accusing my sister of being a thief.
then hopefully he may explain that wasn't what he meant. If it was what he meant then he may re-iterate it, or pretend it wasn't.
If you genuinely think you misunderstood what your friend was saying then say so, and apologise. If you think he misunderstood you, apologise and explain what you really meant.
If, in truth, you don't really believe there has been a misunderstanding at all, then you have two options. You can attempt to re-ignite the fight, or you can let the matter drop, after apologising if you feel the friendship is more important than the argument.
You cannot claim there has been a misunderstanding and than ask for clarification.