In a letter to the company’s clients, managing director Andrew Flintham said the firm has learnt from what happened and is working with its partners to address the issues.
"Tui holidays rely on a complex ecosystem of services," he wrote. "This includes our own pilots and cabin crew, as well as operational partners that cover things like check-in, baggage and catering.
"Over the first weekend of the May half-term, the ecosystem experienced capacity issues that impacted some of our customers. In some instances, customers were subject to delays and – in rare cases – cancellations. These customers had a poor experience – for that, and the distress caused by the cancellations, I apologise."
Flintham said situations like this were rare and the "vast majority" of the brand’s flights operated normally, with more than 200,000 customers taking off as planned.
"Our teams have been supporting customers who were affected in finding alternative holidays and processing any refunds due," he added. "I can assure you that Tui would never leave you stranded overseas.
"I hope this gives you the confidence to look forward to your holiday with Tui this summer, or next time you travel with us. We can’t wait to see you soon."
It comes ahead of a parliamentary committee meeting on Tuesday (14 June), where travel industry bosses will be questioned by MPs about the "flight chaos" faced by holidaymakers during half-term.