Nearly 12,000 passengers were flown back to the UK on Monday, less than 24 hours after the 50-year-old company went bust.
Thousands are being repatriated following the collapse of travel firm Monarch, which has left nearly 2,000 employees out of a job.
Civil Aviation Authority (CAA) chief executive Andrew Haines said the "mammoth operation" has "got off to a good start".
While those already abroad await news of alternative flights home, a further three-quarters of a million people who held future bookings with the firm have had their travel plans cancelled.
Many passengers turned up at airports on Monday morning, only to find their flights were not taking off.
Some couples had their wedding plans thrown into chaos as they struggled to find flights with other airlines for them and their guests.
Sixty-one flights brought 11,843 passengers home from 24 holiday resorts on Monday, the Civil Aviation Authority (CAA) said, in what the Government is calling Britain's biggest peacetime repatriation.
Fifty-eight flights for 11,647 customers were planned on Tuesday.
A total of 110,000 people will be flown home on as close to a normal schedule as possible at no extra cost until October 15, according to the CAA.
Many travellers are in sunshine destinations in Spain and Portugal such as Costa del Sol, the Algarve and the Canary Islands.
Mr Haines said: "We recognise that this will be a concerning time for many customers and we really appreciate their support.
"Given the unprecedented scale of this task, some disruption is inevitable. We thank everyone involved for their patience."
Mr Haines said the CAA was notified by Monarch four-and-a-half weeks ago that "there were issues they were dealing with" and he understood that the firm's board decided to go into administration close to midnight on Saturday.
Monarch was still advertising flights on its website on Sunday, meaning some passengers may have booked trips even after the company's bosses decided it would stop trading.
Customers who have not yet departed will receive a full refund if their booking was protected by the Air Travel Organiser's Licence (Atol).
If it was not - such as some flight-only bookings - they may be able to seek compensation through their travel insurance or credit card company.
Atol is the UK's holiday financial protection scheme and costs £2.50 per customer. By law every UK-based travel company that sells air holidays has to have a licence.
The largest Atol company to stop trading before Monarch was XL Leisure Group in 2008, which had 43,000 people abroad at the time.
Administrators KPMG said 1,858 of around 2,100 people employed across Monarch's airline and tour group had been made redundant after the firm went bust.
Ninety-eight of those made redundant were employed by Monarch Travel Group, while 1,760 were employees of Monarch Airlines.
The remaining employees will help with the administration process, and assist the CAA in bringing holidaymakers abroad back to the UK, KPMG said.
Staff wept and embraced following a meeting at the airline's headquarters near Luton Airport on Monday morning.
The number of customers carried by the company rose 14% in the last year but revenue was down £100 million, while adverse movement of the pound against the dollar had increased costs including fuel, handling charges and lease payments.
In a letter to staff, Monarch chief executive Andrew Swaffield said the "root cause" of the airline's plunging revenues was terror attacks in Egypt and Tunisia, as well as the "decimation" of the tourism industry in Turkey.
Administrators are now considering breaking up the company, which was founded in 1967, as no buyer has been found to purchase Monarch in its entirety.
The group's engineering operation, Monarch Aircraft Engineering Limited, is not in administration and continues to trade normally.