Korean Air Lines' unions have called for the youngest daughter of its chairman, a sister of the infamous 'nut rage' heiress, to step down from management after her alleged abusive behaviour against an advertising agency official caused public outrage.

Cho Hyun-min, also known as Emily Cho and a senior vice president at Korean Air, apologised on Thursday for what she called her "foolish behaviour" after media reports said she threw water at the face of an advertising agency manager during a recent business meeting.

Korean Air said on Friday, in response to media reports Cho had thrown a water bottle at someone's face, said she had thrown either a water bottle or a cup on the floor, but not at anyone's face. On Monday, the airline said it was a cup.

Cho, speaking to TV channel MBC after she cut short a vacation overseas and arrived at Incheon International Airport on Sunday, denied she had thrown a cup of water at the manager's face but said she had "pushed" it.

She said her action was "foolish".

Cho hired a lawyer from one of South Korea's largest law firms, Shin & Kim, to represent her, an official at the law firm said on Monday, after police launched a preliminary inquiry to see whether Cho had abused her power or broken any law.

Korean Air said on Monday it was aware of the police probe. "After we observe the outcome of the investigation, the company plans to take appropriate measures," the airline said.

It is the latest controversy to engulf the owner family of South Korea's largest airline group.

Cho's elder sister Cho Hyun-ah, or Heather Cho, made headlines over a notorious "nut rage" incident in 2014, when she lost her temper over the way she was served nuts in first class before takeoff from New York.

Heather Cho demanded the flight crew chief be expelled from the plane after she was served macadamia nuts in a bag and not on a dish. The South Korea-bound plane had to return to the gate.

Cho was sentenced to one year in jail for violating airline safety laws, but was released after five months. She returned as an executive of Korean Air's hotel affiliate in March.

Her younger sister's tantrum has reignited public impatience with family-run conglomerates known as chaebol, over what some South Koreans see as unchecked bad behaviour by the rich and powerful, especially second and third-generation children of the founders.

"Founders of conglomerates are considered myths, sacred. They have legitimacy, because they built the conglomerates from nothing," said Chang Sea-jin, a business professor at Korea Advanced Institute of Science and Technology.

"But second-generation and third-generation leaders do not have such legitimacy. They are simply born with 'golden spoons' in their mouths," he said.

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