Two Korean Air heiresses will resign from management positions with the family-run conglomerate following abuse of an employee by one of them, the second incident of its kind that has produced widespread backlash.

Korean Air chairman Cho Yang-ho issued a statement Sunday apologising for his daughters' behaviour and said they would both be resigning, Yonhap News Agency reported.

Cho Hyun-ah, recently named president of the airline's hotel business and her younger sister, Cho Hyun-min, a Korean Air senior executive, will be stripped of all their responsibilities, according to Yonhap News Agency.

Former Korean Air senior Vice President Cho Hyun-min, also known as Emily Cho, pictured on June 27, 2014. Photo / AP
Former Korean Air senior Vice President Cho Hyun-min, also known as Emily Cho, pictured on June 27, 2014. Photo / AP

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."

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She was a Korean Air vice president at the time and was sitting in first class aboard a Korean Air flight bound for Seoul when she was given macadamia nuts in an unopened package rather than on a plate, as per the airline's rules, The Washington Post reported. Cho reportedly flew into a rage over the nuts, verbally abusing flight staff and forcing them to apologise on their knees. She then ordered the plane - already taxiing and carrying 250 passengers - to return to the gate and had the offending flight attendants ejected, according to the Washington Post.

In the wake of "nut rage," Cho Hyun-ah was fired by her father and charged with obstructing aviation safety. She was sentenced to a year in prison, but only served a few months, before returning to the company to become president of its hotel business, Yonhap News Agency reported.

Her younger sister, Cho Hyun-min, who also goes by Emily Cho, followed in her footsteps last month when she allegedly verbally abused and threw water at an employee of the airline's advertising agency during a business meeting, Yonhap reported. The Korea Times reported that she was "enraged" at the employee's work performance. She denied throwing water but acknowledged shoving the employee, the BBC reported.

Cho Hyun-min publicly apologised for the fracas, saying her behaviour was "foolish and reckless." The incident is being called "water rage."

"I sincerely apologise for upsetting the general public and employees at Korean Air over issues related to members of my family," their father said in the statement.

The apologies have done little to quell outrage, with many seeing the recent incident as another example of leaders of powerful family-run companies, also known as chaebol, acting with unchecked power, as The Post's Anna Fifield has reported. Cho Yang-ho is chairman of the Hanjin Group, the conglomerate that owns Korean Air.

Protests have grown so heated, some people even petitioned the South Korean president's office to ban the airline from using "Korean" in its name, the New York Times reported.

Police have launched an investigation into the allegations against Cho Hyun-min. The sisters are also being investigated for allegedly using the airline to smuggle luxury goods, furniture and other personal items into the country, the Korea Times reported.

In Sunday's statement, the father attempted to mitigate backlash by announcing the company would establish a "compliance committee . . . prevent reoccurrence of similar incidents," Korea JoongAng Daily reported. He also promised to increase the power of the company's board of directors.

"As chairman of Korean Air and head of a household, I can't help but feel terrible about the immature behavior that my daughter has done," Cho Yang-ho said in the statement. "I am to blame for everything. I apologise to everyone."