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The CEO of Korean Air says his two daughters are resigning after separate incidents that led to allegations of abuse of power inside the company.

Police are investigating the younger daughter, Cho Hyun-min, after she allegedly splashed water in a colleague's face.

Her older sister infamously delayed a flight in 2014 over a packet of nuts - and served jail time for the incident.

In a statement, their father apologised to the public and his employees.

Cho Yang-ho said his daughters would be stripped of all their responsibilities,

Both cases hit the headlines in the country and reopened a national debate about the Korean business system, which is dominated by family firms known as chaebols.

Ms Cho, 36, apologised for her "foolish and reckless behaviour" in the most recent incident earlier this month.

Cho Hyun-min, also known as Emily, who was senior vice-president of the company, reportedly lost her temper because she was unhappy with answers to her questions in a meeting. She denied throwing water but admitted to shoving the advertising agency manager.

Dozens of online petitions to South Korea's presidential website were launched, demanding she be punished.

The airline was already under intense scrutiny after the CEO's eldest daughter, Cho Hyun-ah, known as Heather in English, flew into a rage when macadamia nuts were served to her in a bag and not on a plate on a Seoul-bound flight from New York four years ago.

Ms Cho, 44, was convicted of violating aviation safety, coercion and abuse of power in 2015 and served five months in jail.

She had been back at work for less than month, as an executive of the airline's hotel affiliate, when her father announced her decision to step down on Sunday.

The sisters are granddaughters of the founder of Hanjin Group, one of South Korea's massive family-run business empires.

Their brother, Cho Won-tae, remains president and chief operating officer of Korean Air.

According to Yonhap, the Korean Air offices and homes of the three offspring were searched by police on Thursday amid separate allegations they had avoided paying duties on luxury goods.