"Our IT teams are working tirelessly to fix the problems," British Airways CEO Alex Cruz said in a video posted on Twitter.
"We believe the root cause was a power supply issue and we have no evidence of any cyberattack."
The airline initially canceled only flights before 1 p.m. ET (6 p.m. BST) at Heathrow and Gatwick.
"We are working hard to get our customers who were due to fly today onto the next available flights over the course of the rest of the weekend," the airline said in a statement Saturday afternoon. "Those unable to fly will be offered a full refund."
The system outage -- on Britain's spring bank holiday weekend -- has "affected our call centers and our website but we will update customers as soon as we are able to," the airline said.
"We are extremely sorry for the huge inconvenience this is causing our customers and we understand how frustrating this must be, especially for families hoping to get away on holiday," Cruz said.
The airline posted a statement on its website on Sunday saying "although some of the IT systems have returned, there will be some knock-on disruption to our schedules as aircraft and crews are out of position around the world."
"At this stage we are aiming to operate a near normal schedule of flights from Gatwick and the majority of our Heathrow services," British Airways posted.
British Airways has not outlined how many flights were canceled Saturday, nor how many people were affected.
"Most long-haul flights due to land in London tomorrow (Sunday, May 28) are expected to arrive as normal, and we are working to restore our services from tomorrow, although some delays and disruption may continue into Sunday," the statement said.
In response to tweets from travelers, the airline said it was experiencing a "global system outage" affecting its website, online check-in, contact centers and baggage tracing.
"Working on this as a matter of priority, but if your flight is departing tomorrow you may have to complete check in at the airport," it tweeted to one customer.