Smith added in his post that, "Violence in all forms is poisonous and destructive."
Will Smith has issued an apology for striking presenter Chris Rock at Sunday's Academy Awards, a report by CNN said.
In a post on Instagram on Monday afternoon, Smith called his behaviour "unacceptable and inexcusable".
He said, "Jokes at my expense are a part of the job, but a joke about Jada's medical condition was too much for me to bear and I reacted emotionally.
"I would like to publicly apologise to you, Chris. I was out of line and I was wrong. I am embarrassed and my actions were not indicative of the man I want to be. There is no place for violence in a world of love and kindness."
Smith added in his post that, "Violence in all forms is poisonous and destructive."
He also included in his note an apology to "the Academy, the producers of the show, all the attendees and everyone watching around the world," as well as the family of tennis stars Venus and Serena Williams and those involved with the film for which he won his best actor award on Sunday.
"I deeply regret that my behaviour has stained what has been an otherwise gorgeous journey for all of us," he wrote. "I am a work in progress."
Smith slapped Rock during the Oscars ceremony after the comedian told a joke about his wife.
Around 40 minutes later, Smith would take the stage again — this time as a winner.
Accepting his best actor award for his role in "King Richard," a tearful Smith acknowledged the earlier incident and apologised to the Academy of Motion Pictures Arts and Sciences, the organisation behind the Oscars, and fellow nominees.
Following the ceremony, the Academy Awards tweeted a short statement about the on-stage incident that read: "The Academy does not condone violence of any form. Tonight we are delighted to celebrate our 94th Academy Awards winners, who deserve this moment of recognition from their peers and movie lovers around the world."
The Los Angeles Police Department also said Rock chose not to press charges against Smith over the onstage altercation.
By midday on Monday, the Academy issued a stronger statement, this time condemning Smith's actions and revealing they had started a "formal review around the incident."
It added that it "will explore further action and consequences in accordance with our Bylaws, Standards of Conduct and California law."
At least a dozen members of the Academy met virtually on Monday morning to discuss a response to Smith slapping Rock, according to two sources with knowledge of the meeting.