They also confirmed that Chris Rock has still not filed a report over the incident where 53-year-old Smith climbed on to the stage and slapped him in front of a stunned live audience and millions more around the world.
Smith issued the apology on Instagram just after midday Tuesday (NZT), directly addressing Rock and his violent assault on the comedian, who had made an off-colour joke about Smith's wife Jada Pinkett-Smith during the ceremony.
Smith wrote: "Violence in all of its forms is poisonous and destructive. My behaviour at last night's Academy Awards was unacceptable and inexcusable. 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."
He continued by calling his actions toward Rock "wrong" and admitting he was out of line.
"I would like to publicly apologize 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 then issued an apology to the Academy and also to the Williams family.
"I would also like to apologize to the Academy, the producers of the show, all the attendees and everyone watching around the world. I would like to apologize to the Williams Family and my King Richard Family. I deeply regret that my behaviour has stained what has been an otherwise gorgeous journey for all of us.
"I am a work in progress," he concluded.
The apology followed a chaotic Academy Awards ceremony, in which Smith was named Best Actor for role in the movie King Richard, a movie based on the lives of Serena and Venus Williams and their father.
Many labelled the actor's acceptance speech as "insincere" with no apology being made to Rock.
The post came just hours after the Academy body said it "condemns" Smith's assault of Chris Rock during the 94th Oscars ceremony.
It also revealed it had now launched a formal review of the incident and said it would "explore further action and consequences" in accordance with California law, and the body's standards of conduct.
The Academy leadership strongly considered removing Smith from the broadcast following the incident, a source told CNN.
"There were immediate discussions but the Academy decision-makers were seated in various spots in the Dolby Theater and couldn't mobilise to make a decision before he won best actor," the source said.