In a YouTube video released Friday night, Target CEO Gregg W. Steinhafel offered a 10 percent discount to all customers this weekend, apologizing to customers who were affected by a massive data breach involving millions of credit and debit cards.

On Thursday, Target confirmed that someone had hacked into its systems and had stolen 40 million debit and credit cards from stores across the country. The breach apparently lasted from Black Friday to Dec. 15.

As expected, the thieves are using that information obtained from those credit cards to make phony copies that are being sold on black market stores around the world, KrebsonSecurity found.

"We're in this together, and in that spirit, we are extending a 10 percent discount - the same amount our team members receive," Steinhafel wrote in a statement on Target's website.

Groceries are eligible for the discount, though video games, gift cards, mobile phones and a few other items are excluded.

Steinhafel said the company would offer free credit monitoring services and downplayed the impact the breach might have on customers.

"We want our guests to understand that just because they shopped at Target during the impacted time frame, it doesn't mean they are victims of fraud," he said. "In fact, in other similar situations, there are typically low levels of actual fraud."

He promised that the guests would "not be held financially responsible for any credit or debit card fraud."

Separately, Target spokeswoman Molly Snyder said in a written statement that "we are hearing very few reports of actual fraud."