The actor claimed he had 'reached out' to Rock since the incident took place in March, but learned he is 'not ready to talk'.
"When he is, he will reach out," Smith said, adding: "I will say to you, Chris: I apologise to you.... and I'm here whenever you're ready to talk."
Rock appeared to make reference to the video during one of his stand up routines last week, but a source close to the comedian indicated to Entertainment Tonight he currently doesn't have any intention of directly responding to Smith.
The insider claimed Smith would 'love nothing more' than if Rock publicly accepted his apology, but stressed: "Chris has no plans to reach out to Will."
They went on to suggest Smith timed the apology, which came after the actor resigned from the Academy, to be in his own best interests, saying: "He needs the public's forgiveness, not Chris."
Rock has largely remained quiet about being slapped by Smith on stage at the Oscars, and has only briefly addressed the matter while speaking to audiences on his Chris Rock Ego Death World Tour.
Addressing the crowd just hours after Smith released his video, Rock commented: "Everybody is trying to be a... victim.
"If everybody claims to be a victim, then nobody will hear the real victims. Even me getting smacked by Suge Smith…I went to work the next day, I got kids. Anyone who says words hurt has never been punched in the face."
Smith told the public in his video that his actions took a personal toll on him, saying: "I hate when I let people down. So it hurts, it hurts me psychologically and emotionally to know I didn't live up to people's image and impression of me.
"And the work I'm trying to do is, I am deeply remorseful and I'm trying to be remorseful without being ashamed of myself. I'm human and I made a mistake, and I'm trying not to think of myself as a piece of s**t."
LADbible has reached out to representatives for Rock for further comment.
Featured Image Credit: ZUMA Press, Inc./Alamy Stock Photo/Will Smith/YouTube