Cruz said a power surge, had "only lasted a few minutes", but the back-up system of the airline had not worked properly.
He said the IT failure was not due to technical staff being outsourced from the UK to India.
Cruz told the BBC that he will not resign and that flight disruption had nothing to do with cutting costs.
"I can confirm that all the parties involved around this particular event have not been involved in any type of outsourcing in any foreign country," he told Sky News.
BA's GMB union has said outsourcing IT jobs to India could have made the problems worse.
The union spokesperson said it could have been avoided had "hundreds of dedicated and loyal" not been replaced by cheaper Indian staff in 2016.
Cruz also said that no BA passengers' data had been compromised in the IT meltdown and said there was no evidence it was the result of a cyber attack, promising not to allow such an outage to happen again.
The IT failure was caused by a short but catastrophic power surge at 9.30 am on Saturday that affected the company's messaging system, he said, and the backup system failed to work properly.
"We have no evidence whatsoever that there was any cyber attack of any sort."
Cruz said he was "profusely sorry" to the thousands of passengers still stranded at airports worldwide.
He claimed two thirds of passengers will have reached their destination by the end of the day.
The BBC also reported of a leaked staff email revealed Cruz had told staff not to comment on the system failure.
When asked about the email he told the public broadcaster that the tone was clear: "Stop moaning and come and help us".
The airline is now close to full operational capacity after the problems resulted in mass flight cancellations at Heathrow and Gatwick over the weekend.
The airline cancelled 13 short-haul flights at Heathrow today.
Heathrow, Europe's busiest airport, advised affected BA passengers not to travel to the airport unless their flights had been rebooked, or were scheduled to take off on Monday.
Passengers on cancelled flights have been told to use the BA website to rebook.
BA is liable to reimburse thousands of passengers for refreshments and hotel expenses, and travel industry experts have suggested the cost to the company - part of Europe's largest airline group IAG - could run into tens of millions of pounds.
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