The 51-year-old was released a year later on appeal but is currently undergoing a retrial.
"We are recognised for our top-class technology and products but the public eye towards Samsung is still critical," Lee said. "This is all because of our shortcomings. This has been my fault and I offer my sincere apology," he added.
He promised there would be "no more controversy" over his promotion, pledging: "I will never take any actions that go against the law."
Lee bowed three times before flashing cameras at a Samsung Electronics office in Seoul, where reporters sat apart under coronavirus distancing rules.
Speaking in steady tones and swallowing occasionally, Lee - whose grandfather founded the Samsung Group - said he would end the line of family succession.
"I do not plan to pass down my role to my children," he said. "This is something I have thought about for a long time but have been hesitant to express it openly." Wednesday's apology came at the request of Samsung's compliance committee, which oversees the firm's transparency in its corporate dealings.