This follows public and industry criticism at the way the situation has been handled over the past nine years. After the chief executive initially refused to apologise at an inquest hearing, Thomas Cook faced heavy backlash across social media.
Earlier this week, Fankhauser announced that compensation Thomas Cook received would be donated to charity and publicly apologised.
"I’m a deeply sorry – as a father myself – about he tragic deaths of Bobby and Christi Shepherd in 2006 on a Thomas Cook holiday," he said.
"It is absolutely clear that there are things that we as a company could have done better during the past nine years – in particular how we have conducted our relationship with the family."
Neil Shepherd and Sharon Wood, the parents of Bobby and Christi, had previously hit out at the travel firm after a UK inquest concluded Thomas Cook had breached its "duty of care" to the family.
"It is disgraceful that after all we’ve been through Thomas Cook is still putting us last in the equation. We haven’t had this so-called letter of apology. We have been shown it by the press and feel it is an appalling continuation of Thomas Cook’s PR exercise. It’s not an apology for its wrongdoing but a general offer of sympathy," the family statement read.
Thomas Cook told PRWeek that it had nothing more to add at this time, stating that it would not be discussing the details of private discussions.