The airline said it intends to run a full schedule at Gatwick today and to operate a full long-haul schedule and a "high proportion" of its short-haul programme at Heathrow.
BA passengers have been told to check the status of their flights before travelling to the airports where scenes of chaos unfolded over the weekend.
The airline claimed it was making "good progress" in recovering from the worldwide IT glitch.
"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," Sky news quoted a BA spokeswoman said:
"We apologise again to customers for the frustration and inconvenience they are experiencing and thank them for their continued patience."
— British Airways (@British_Airways) May 28, 2017
The company said there was no evidence the failure was the result of a cyber attack.
Experts predict the knock-on effect could continue for several days and BA is facing huge compensation costs, with reports suggesting the bill could top 100 million pound.
Passengers faced hours-long lines to check in, reclaim lost luggage or rebook flights at Terminal 5, BA's hub at Heathrow.
Alex Cruz, the airline's chairman and CEO, issued a video message on Twitter to reassure passengers about their lost luggage and apologise.
Alex Cruz, BA chairman and CEO, apologised to customers in a video message on Twitter and said, "I know this has been a horrible time for customers. Some of you have missed holidays, some of you have been stranded on aircraft, some of you have been separated from your bags. Many of you have been stuck in long queues whilst you waited for information.
"On behalf of everyone at BA I want to apologise for the fact that you had to go through these very trying experiences."
BA operates hundreds of flights from Heathrow and Gatwick on a typical day - and both are major hubs for worldwide travel.
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