The 56-year-old filmmaker caused outrage after he cast his friend, registered sex offender Steven Wilder Striegel, who had served time behind bars for trying to coax a 14-year-old girl into a sexual relationship over the Internet in 2010, in the new movie.
Munn discovered Striegel's criminal past last month, and successfully lobbied Twentieth Century Fox bosses to cut the scene, and the news went public last week. Munn went on to accuse Black of keeping the news from the cast and crew, and complained that she had been shunned by her co-stars.
At "The Predator" premiere on Wednesday, Black reached out to Munn, and became visibly emotional as he discussed the controversy.
"I have reached out to Olivia," he told Entertainment Tonight. "I felt that I owed her that call, that apology and I'm very sorry for any pain that she's felt, but I reached out privately."
The director expressed his remorse over the decision to cast Striegel, and took full responsibility for the fallout.
"If I caused pain, it's on me. It's my fault. I made a decision, which was a very bad - look, it's not about the fact that I was as shocked to discover what's going on at reading these horrible things in the paper. That's still on me," he continued.
"I'm not allowed to just treat this like we're kids in college and putting friends in movies because this is big leagues, and I felt like I had let people down and caused pain to the cast and that is not acceptable."
Munn told ET at the event that she had been encouraged by the response to her actions, and was happy that her co-stars - including Sterling K. Brown - had finally supported her.
"Just to have everyone on that same page... that's honestly been the most amazing thing just to see that."