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The head of retail powerhouse Target is pledging to "make significant changes" in the wake of the latest revelation that as many as 110 million customers were ensnared in a massive data heist at stores across the country.

"Clearly, we're accountable and we're responsible. But we're gonna come out at the end of this a better company," Gregg Steinhafel — Target chairman, president and chief executive officer — told CNBC's Becky Quick in an exclusive interview that will air in full on Monday morning. "And we're gonna make significant changes."

Steinhafel said that the embattled company will "get down to the bottom of this," adding: "We are not gonna rest until we understand what happened and how that happened." He also apologized for the sweeping theft, saying: “I’m personally very sorry that this whole event even happened.”

The retailer has said at least 70 to 110 million customers — a more massive number than previously disclosed in December, when the breach was first reported — were struck by the holiday-season data theft, making it one of the largest security breaches of its kind.

The stolen data includes names, mailing addresses, phone numbers or email addresses for up to 70 million individuals.

And Steinhafel told CNBC that the company still doesn't yet "know the full extent of what transpired."

"But what we do know was there was malware installed on our point-of-sale registers. That much we've established," he said. "We removed that malware so that we could provide a safe and secure shopping environment."