Lastminute.com had promised to refund people for package holidays cancelled due to the Covid-19 pandemic.
But it missed a repayment deadline at the end of January.
The Competition and Markets Authority (CMA) said the company needed to pay people back within seven days to avoid court action.
“It is wholly unacceptable that thousands of Lastminute.com customers are still waiting for full refunds for package holidays despite the commitments the company signed with us,” said CMA chief executive Andrea Coscelli.
“We take breaches of commitments extremely seriously. If Lastminute.com does not comply with the law and pay people their outstanding refunds quickly, we will take the company to court.”
Lastminute.com has been approached for comment. Last week, the online travel agent said the refund process had been “very complex and difficult”.
In December, Lastminute.com made a commitment to the watchdog to pay out more £7m to more than 9,000 customers when their holidays were cancelled due to the pandemic.
People were supposed to get their money back by 31 January, but Lastminute.com still owes more than £1m to 2,600 customers, the CMA said.
The travel agent also told some of those package holiday customers to go directly to their airline to get the cost of their flight back, which the regulator said it was not supposed to do.
Consumer group Which? said Lastminute.com had been “one of the worst culprits when it comes to failing to refund customers for coronavirus cancellations”.
Which? had called on the CMA to uncover how many people had not been refunded in time.
Rory Boland, editor of Which? Travel, said the regulatory action sent “a clear message that this kind of behaviour is unacceptable”.
“Lastminute.com is one of countless holiday operators that have let customers down on refunds, highlighting the need for widespread reforms across the travel industry,” he said.