London(CNN) British Airways is planning to have a "high proportion" of its flights operating Monday after it was forced to cancel Saturday flights out of London's two biggest airports.
A "major IT system failure" caused severe disruption to the airline's flight operations worldwide, leaving thousands of passengers stranded.
On Sunday, the airline said that it would aim to resume a "full schedule" at Gatwick as well as the majority of services from Heathrow.
It also said it would refund those who suffered cancellations and no longer wanted to fly to and from the affected airports.
"We operated a full schedule at Gatwick on Sunday. At Heathrow, we operated virtually all our scheduled long-haul flights, though the knock-on effects of Saturday's disruption resulted in a reduced short-haul programme" the airline said in a statement Sunday.
The airline asked travelers not to go to Heathrow unless they are confirmed for travel, not even to pick up delayed baggage.
"As our IT systems move closer to full operational capacity, we will again run a full schedule at Gatwick and intend to operate a full long-haul schedule and a high proportion of our short-haul programme at Heathrow," the airline said.
British Airways has extended its flexible booking policy and says customers can rebook their flights to travel up to and including June 10.
On Saturday, British Airways CEO Alex Cruz posted a video on Twitter in which he said he believed the cause of the problem to be a power supply issue.
He also rejected any notion that the airline had been the subject of a cyberattack.
The airline had initially canceled only flights before 1 p.m. ET (6 p.m. BST) at Heathrow and Gatwick.
Travelers complained of being overcharged hundreds of dollars for hotels.
"Two-star flea bag hotel near Heathrow charging £800 for a single room!" David Lane tweeted.
Travelers in the United Kingdom were already reporting disruptions, including baggage and flight delays, when the airline reported serious computer problems around midday Saturday.
Paddy Anigbo, a Nigerian national visiting his wife in the United Kingdom on their wedding anniversary, said his plane sat on the tarmac at Heathrow for about four hours after landing. The plane's entertainment system and air conditioning were operating, and free snacks and drinks were served.
But, he told CNN by phone: "No alcohol, which is wise. You don't want that kind of chaos."
"There's no real frustration," Anigbo, an IT specialist, said while still on the tarmac. "I mean, the frustrations are there. We all want to get off the plane and go home."
Anigbo praised the flight crew and lamented that the pilot, at one point, announced that he would give hourly updates.
When Anigbo's plane finally reached the gate, he described the scene as "chaos."
Gareth Ebenezer, who was on his way to Dublin to watch a rugby union final, told CNN he gave up and went home after getting caught up in the chaos at Heathrow.
Ebenezer saw lots of slow-moving lines, with some people asked to wait outside Terminal 5, he said. Most travelers seemed resigned, he said, though others appeared stressed and some children were crying.
Most people were being rebooked on Sunday flights, he said, but by then, he'd already have missed his match.
"BA staff were slow on announcements and updates, and were bringing out cordons and bottles of water to manage queues," Ebenezer said. "They seemed incapable of doing anything else, despite their best intentions, due to the system outage. They were totally crippled."
Some stranded passengers used Twitter to voice their frustrations.
Filmmaker Philip Bloom tweeted that he was stuck on the tarmac at Heathrow after his delayed flight from Belfast, Northern Ireland, finally landed because there was no space for the aircraft to park.
Bloom later tweeted, "9 hours after checking in at Belfast airport we get home after the chaos of the British Airways IT crash."
Computer glitches and outages have plagued BA and other airlines in recent months.
In September, British Airways said a computer problem in its check-in systems caused delays and long lines at numerous airports.
Delta was hit by a global computer outage one month earlier that caused days of travel chaos, including about 2,000 flight cancellations.
And in July, Southwest Airlines canceled more than 1,000 flights following a system failure.