The daughter of Korean Air's CEO visited a cabin crew chief Sunday to apologise for kicking him off a plane over the way she was served some nuts, as allegations emerged that she forced him to kneel and ask forgiveness.

Cho Hyun-Ah, a top executive at Korean Air, resigned Tuesday from all her posts at the family-run flag carrier in the face of an intense public backlash and escalating investigations by state authorities.

The 40-year-old forced a New York-Seoul flight to return to the terminal and eject the head of cabin crew on December 5 after she took exception to the arrival of some macadamia nuts she had not asked for, and to the fact they were served in a packet rather than a bowl.

Cho, sitting in first class, forced cabin manager Park Chang-Jin and a female attendant to kneel in front of her, calling Park names, pushing him into the cockpit door and jabbing him with a service manual, according to his account of the incident.

Cho visited the homes of both staff members on Sunday morning to offer a personal apology, but neither was home so she left notes at their doors saying sorry, a company spokeswoman told AFP.

Cho has denied that she forced the pair to kneel. "I've never heard such thing. I don't know anything about it," she said when reporters asked her to confirm claims made by Park in an interview with Seoul's KBS television station broadcast Friday night.

Another passenger who was sitting in first class on the flight confirmed most of Park's account and said she saw the two attendants on their knees.

"I felt so sorry for the flight attendants, who looked totally terrified at her," the passenger told KBS after meeting with Seoul prosecutors Saturday to give testimony over the incident.

Park said in his interview with KBS that the incident had been deeply humiliating.

"You can't imagine the humiliation I felt unless you experience it yourself," he said.

"She said, 'Make contact (with air traffic control) right now to stop the plane. I'm not going to let this plane go.' How could I disobey the daughter of the owner in a situation like that?" Park said.

He has also claimed that Korean Air officials had for the past week pressed him to blame himself over the incident. The airline declined to comment on the allegation.

Cho's behaviour sparked huge criticism in South Korea, where she has been accused of being petty and arrogant, and prompted the transport ministry and Seoul prosecutors to launch investigations into whether she breached aviation safety laws and caused disruption to business.

Korean Air CEO Cho Yang-Ho gave a televised press conference Friday to apologise for his daughter's "foolish act" and suggested he should share some of the blame for not bringing her up correctly.

"I failed to raise the child properly. It's my fault," he said.

The incident, which has been branded "nutgate" on social media, delayed the departure from New York by about 20 minutes. It arrived 11 minutes late in Seoul.