The chairman of Korean Air Lines has apologised to a country brimming with outrage over an incident in which his daughter delayed a flight because she was unhappy with the way a flight attendant served her nuts.

Cho Yang-ho also said his daughter, who was an executive at South Korea's flag carrier in charge of in-flight service until she quit this week, was being removed from all posts at affiliate companies.

His public apology came shortly before his daughter was expected to appear before authorities to answer questions about an incident at New York's John F. Kennedy airport.

Heather Cho, 40, is also under a separate investigation by local prosecutors following a complaint filed by a civic group that accused her of breaking multiple laws.

"I apologise to the people of this country as chairman of Korean Air and as a father for the trouble caused by my daughter's foolish conduct," said Cho, who bowed deeply in front of a media horde gathered in the lobby of the airline's headquarters near Seoul's Gimpo International Airport.

The incident was first reported on Monday and public outrage grew after Korean Air issued what many in the country took to be a half-hearted apology that rationalised her conduct in the face of inadequate performance by the cabin crew chief.

Cho, who was seated in first class on the South Korea-bound flight, was displeased with being served macadamia nuts in a bag and not a dish. The pilot brought the plane back to its gate for the cabin crew chief to be expelled.

The Airbus A380 arrived at Incheon, near Seoul, 11 minutes behind schedule.

The Transport Ministry said it was reviewing whether Heather Cho violated aviation laws. She could face prosecution and a fine if found to have committed wrongdoing, an official said.

Investigators searched the offices of Korean Air on Thursday.

"I am sorry I did not educate her well," her father said.

The incident has stoked both mirth and anger in South Korea, whose economy is dominated by powerful family-run conglomerates known as chaebol.

Local sales of macadamia nuts reportedly surged in the days following news of the incident.

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