SEOUL (AFP) - The second daughter of Korean Air's chief executive apologised Wednesday for swearing "revenge" in a text message to her sister, who has been arrested for delaying a flight with a tantrum over snacks.

The message reading "I will certainly take revenge!" was sent by Ms Cho Hyun Min, 31, on Dec 17 when Korean Air (KAL) heiress Heather Cho Hyun Ah was summoned by prosecutors for questioning.

Prosecutors revealed its contents late on Tuesday after Heather Cho was formally arrested on charges including violation of aviation safety law, coercion and interference in the execution of duty, Yonhap news agency said.

"I'm really sorry beyond words for my text message... I would not make any excuses. It's all my fault," Ms Cho Hyun Min, who holds executive-level positions at the flag carrier and its sister companies, wrote on Twitter. The subject of her vengeance was not clear, but Yonhap and newspapers speculated she was talking about the chief purser, who has criticised Heather Cho in TV interviews.

The 40-year-old Heather Cho has been accused of forcing the chief purser off a Dec 5 New York-Seoul flight and of compelling the taxiing plane to return to the gate so he could disembark in a case that has caused uproar in South Korea.

Cho had also taken exception to being served macadamia nuts she had not asked for - and in a bag, not a bowl.

Korean Air's reputation has been hit hard by the detention of the chief's daughter and another unidentified company executive, who was accused of destroying evidence from the incident.

Heather Cho - one of three children of boss Cho Yang Ho, who is also the patriarch of business conglomerate Hanjin Group - has publicly apologised and resigned from all her posts in the organisation.

The Transport Ministry has vowed to sanction the airline with a flight ban, most likely on the New York-Seoul route, that could last for up to a month, or with fines of up to US$2 million (S$2.6 million).

Separately, the ministry has vowed to punish eight of its officials after admitting their investigation into the incident was unfair.

On Monday, Mr Shin Un Chul, a ministry auditor, said the inclusion of airline staff in the probe may have intimidated witnesses.

Four of the eight officials who questioned Heather Cho will receive a warning, while the others will be referred to a disciplinary committee and could face dismissal.

A ministry investigator was arrested last week for leaking details of the investigation to Korean Air officials.