Civil Aviation Authority consumers and markets director Paul Smith said “we are very sorry” and promised the organisation was “working tirelessly” to process payments.
More than 50,000 customers were still owed money, despite £160 million having already been refunded, he told the BBC.
Incomplete claim forms and attempted fraud were adding to delays, he said.
Thomas Cook collapsed on September 23 after failing to obtain rescue funds from its banks.
Some 150,000 holidaymakers abroad had to be flown back to the UK during a two-week operation run by the CAA.
A refund process was opened on October 7 for Atol-protected customers.
Although the CAA said it expected to pay the tens of thousands of people who registered on the first day within 60 days, only about two-thirds were refunded by the weekend deadline.
Smith said: “This is the biggest refund operation in UK travel. We have paid out already about £160 million, and expect over the next couple of days to get that up above £180 million.
“We have had to put some extra checks in because we were concerned about fraud. And we had some challenges with the data we received from the company. We are sorry for those people we have not yet been able to pay.”
Some claimants had provided incomplete forms, and he urged them to update the details as soon as possible.
“We really want to make these payments as quickly as we can because it is money people are entitled to,” Smith added.
Some 300,000 Thomas Cook claims have been received so far, 215,000 of which have been confirmed as valid.
However, this figure includes about 90,000 direct debit customers in October whose money was automatically returned.
Podcast: ‘Heroes of the high street’ John and Irene Hays