From a man's perspective: we are pretty vain... So when we've had an argument, and it wasn't our fault, then we wouldn't apologize for it...
Anyways, the best thing you could do now is just to talk about it. He's feeling something he doesn't really know how to handle, which is apparent seeing that you've already apologized and he's still acting this way, so you should facilitate him into getting through this and sorting it out.
Call him up and ask something like "Hey, you've been pretty quiet for the past few days, is anything wrong?"
If he tells you what's wrong, guide him through it. "Gosh, I can't imagine how that must feel to you... How do you feel about that?"
"I can totally understand that."
Then, if he's emptied his mind, if he's thrown his feelings on the table, and when you UNDERSTAND HIM, then you can go about into clearing up the thing you have, and to apologize one final time. Do tell him how you've felt about this, how you feel now, and how you'd want the future to be ("I hope we can discuss our problems without arguing next time... I really like you, so I don't like to see you mad", for example).
After that, of course, end on a positive note, and ask him "alright, so when are we going to see each other again? I have an awsome movie I want to see with you."
Anywhoo, good luck with this stuff. I'm sure everything'll be fine. Do tell us how it went when you've done it, mmkay? ;p
Have a great day! ^^