The airline is expecting to run a full schedule today from Heathrow and Gatwick airports but said it still had "work to do" reuniting bags with passengers.
BA's chief executive Alex Cruz said a full investigation would take place into the failure which affected 75,000 passengers.
A 'significant number of customers' are still without their luggage after BA IT systems failure
"On Saturday morning at around 9.30 there was indeed a power surge that had a catastrophic effect over some communications hardware which eventually affected all the messaging across our systems.
We have no evidence whatsoever that there was any cyber attack of any sort
Alex Cruz – BA chief executive
"We will have completed an exhaustive investigation on exactly the reasons of why this happened. We will, of course, share those conclusions once we have actually finished them.
"We have no evidence whatsoever that there was any cyber attack of any sort."
On Saturday night, travellers spent the night sleeping on yoga mats spread on terminal floors after BA cancelled all flights leaving the London hubs, while disruption continued into Sunday with dozens more services from Heathrow axed.
BA's chief executive Alex Cruz said a full investigation would take place
The IT outage had a knock-on effect on BA services around the world, while passengers who did get moving on the limited number of flights to take off from the UK reported arriving at their destinations without their luggage.
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The disruption also hit transport systems on the ground, with hundreds of travellers flooding London's King's Cross station in hope of boarding a train north instead.
Mr Cruz said the outsourcing of jobs was not to blame for the "catastrophic" IT failure.
BA was accused of greed after the GMB union suggested the disruption could have been prevented if the beleaguered airline had not cut "hundreds of dedicated and loyal" IT staff and contracted the work to India in 2016.
In a statement, the airline said: "We are continuing to make good progress in reuniting bags with customers around the world who were affected by the major IT systems failure on Saturday.
"Although we have already flown many bags to the correct airport, there is still some work to do and we know there are still significant numbers of customers who are yet to receive their luggage.
On Saturday night, travellers spent the night sleeping on yoga mats spread on terminal floors Electronic devices BANNED on flights Fri, March 24, 2017
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"We are very sorry for the frustration this situation is causing at a very busy time of year for holidays."
Meanwhile, the airline has come in for criticism after signposting some customers to a phone line costing up to 62p per minute.
BA's Twitter account suggested a number of passengers should call 0844 493 0797 – which can cost up to 7p per minute plus access charge of up to 55p per minute.
David Hickson, of the Fair Telecoms Campaign, told the Sun: "BA is being greedy and foolish. The Fair Telecoms Campaign calls on all users of 084 numbers to cease this foolishness."
The airline said it has a freephone number – 0800 727 800 – for people affected by the IT failure
The airline said it has a freephone number – 0800 727 800 – for people affected by the IT failure.
A spokeswoman added: "As a global airline that flies to and from more than 170 airports worldwide, we have call centres placed strategically around the world in the UK, Europe and Asia.
"Customers can also add phone charges into any claims they submit and we'll look at them."