In the tweets, Cumia said called his alleged attacker a "cunt animal" and said black people were "uncivilized.
On Sunday, Cumia said he wasn't talking about African-Americans.
“I was talking about people that instantly go to violence," he said.
He said he won't apologize, even if doing so would get him his job back.
“I will never apologize for this,” he said. "I didn’t do anything wrong. This is completely — this is exactly who I am. I am not seen going to deny it. I go off on tears like this. I curse, I say horrific things about people that piss me off and that’s exactly what I did. Why am I going to apologize and say I am different or I changed? I haven’t. It would be a phony bogus apology. If it happened again, I would do the same thing.”