Around one in three of the first Thomas Cook customers to claim refunds will not be paid within the 60-day target, according to the UK aviation regulator.
More than 22,000 people who submitted their online forms on the opening day of the Atol refund programme cannot be paid until they provide additional information, the Civil Aviation Authority (CAA) said.
The scheme was launched on October 7 and the CAA initially aimed to pay all valid claims within 60 days, which falls today.
The regulator insisted it wants to issue refunds "as soon as possible" and urged claimants to check their email junk and spam folders if they have not heard anything by the end of the week.
About two-thirds of the 67,000 legitimate claims made on the first day will be paid "by the weekend", according to the organisation.
An additional 90,000 direct debit customers were refunded in October, meaning the amount of money paid back so far has reached nearly £160m.
The CAA has not received claims relating to around 40,000 of the 300,000 cancelled holidays eligible for a refund.
Customers have until September next year to submit the online form.
"We thank consumers for their ongoing patience as we continue to do all that we can to work through the UK travel industry's largest ever refunds programme," CAA's chief executive Richard Moriarty.
"I appreciate that this is a concerning time for Thomas Cook customers who are waiting for their refunds, particularly at this time of the year.
"We will have already paid out more than £160m by this weekend and will continue to pay claims as soon as possible," he added.
"Where we have had to request further information, we encourage those consumers to respond at the earliest opportunity so that we can finalise these payments. I would like to reassure consumers that all valid Atol-protected payments will be refunded," he added.
Thomas Cook collapsed on September 23, putting 9,000 UK jobs at risks and disrupting the travel plans of one million holidaymakers with future bookings.
Around 140,000 passengers already on holidays were brought home by the CAA over a two week period.