The Korean Air chief added his two daughters will immediately step down from all positions within the company.
In 2016, the FTC imposed a fine of 1.43 billion won (US$1.2 million) on Korean Air Lines for similar unfair practices involving two of its affiliates.
Korean Air chairman Cho Yang-ho has apologised for the behaviour of his two daughters Cho Hyun-Min and Cho Hyun-ah following different controversies, reported AFP.
Chairman Cho has also apologised for the behaviour of his youngest daughter, the airline's senior vice president Hyun-min, after she allegedly threw water over an official attending a business meeting.
Chairman Cho said the company would "turn over a new leaf" with stronger management led by its board.
In 2014, Cho Hyun Ah, also known as Heather Cho, was jailed for five months for ordering a Korean Air plane to return to its gate at a NY airport after she was angered over the way a packet of macadamia nuts was served to her in first class.
The notorious heiress was jailed but had returned to work as an executive of Korean Air's hotel affiliate in March.More news: Quickfire Amir Khan wins comeback against Phil Lo Greco in 40 seconds
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Cho Hyun-ah, also known as Heather Cho, rose to global infamy in 2014 after an incident at John F. Kennedy International Airport that has since been dubbed "nut rage". According to The Straits Times, in the process of kicking the crew member off the plan, Cho Hyun-ah also made a taxiing plane return to its gate, causing a flight delay in the process.
Police have launched an investigation into the allegations against Cho Hyun-min.
Media reports accused Lee, who is in her late 60s, of a litany of abuse of multiple workers renovating her home and of Korean Air employees, including screaming, cursing, slapping and kicking.
She was sentenced to a year in prison, but later freed after an appeals court cleared her of the most of hampering an air route.
The share price of Korean Air, despite gaining 2.7 per cent Monday afternoon, has lost about 5 per cent since April 12, when the "water rage" scandal first flared up.
"As chairman of Korean Air and as the head of my family, I feel crushed by the immature behavior of my daughters".
Ms. Cho said she had thrown the water on the floor, not at the official's face, but nevertheless apologized for what she called foolish and reckless behavior.