Peter Fankhauserissued a public apology to the parents as the company seeks to halt mounting damage to its reputation over the way it has treated the family since the incident.
He said: “I’m deeply sorry — as a father myself — about the tragic deaths of Bobby and Christi Shepherd in 2006 on a Thomas Cook holiday.
“It’s absolutely clear that there are things we as a company could have done better during the last nine years — in particular how we have conducted our relationship with the family.”
Speaking after the release of Thomas Cook’s half-year results, Fankhauser also vowed to apologise directly to the family of Bobby and Christi, from Horbury, near Wakefield, who died at the Louis Corcyra Beach Hotel on the Greek holiday island in 2006 when they were overcome by fumes from a faulty boiler.
Some customers have threatened to boycott the firm after it emerged it received around £3m (€4.2m) in compensation from the hotel chain responsible for the incident, and following criticisms from the family.
Thomas Cook said earlier this week it would donate £1.5m to the charity Unicef, while the remaining £1.5m went to its insurers for underwriting legal fees.
But the children’s parents, Neil Shepherd and Sharon Wood, hit out at the firm, saying they had not been consulted by Thomas Cook about the donation to Unicef.
The family have a particular children’s charity they have been supporting and to which relatives and friends have been donating in Bobby and Christi’s memory.
Last week, a jury at the inquest gave a conclusion of unlawful killing and said Thomas Cook “breached their duty of care”.
Following the inquest, the family blasted the firm for failing to apologise directly, saying it was “disgraceful” an apparent letter of apology from Fankhauser was only brought to their attention by journalists.
In an investor presentation following the firm’s half-year figures, Fankhauser said he wanted to make amends. “You will understand that I’m not going to repeat the mistakes of the past by talking about the family in public and my intention is to see how we can help them move on with their lives,” he said.
Fankhauser, who took over as Thomas Cook’s chief executive in November, told the Financial Times that bookings had not been affected by the mounting public backlash over its handling of the carbon monoxide tragedy.
Bobby and Christi, aged six and seven, died when they were overcome by fumes from a faulty boiler as they stayed in a bungalow in the grounds of the hotel with their father and his partner, now wife, Ruth, in October 2006.