In an exclusive CNBC interview that aired Monday, Target Chairman and CEO Gregg Steinhafel said he supports the movement to a chip and PIN-number system called EMV technology that replaces vulnerable magnetic strips.
(Read more: 'I'm still shaken'by Target data breach, says CEO)
But switching the entire payment system will be difficult and expensive—and it likely won't happen for shoppers in the U.S. until the end of 2015.
Lundgren didn't say whether he supports that EMV system, but stressed: "The retailers, the banking industry, [and] the credit card industry should be working very closely together to figure out what is the right technology to protect the consumers … and then work around the solutions from there."
On Dec. 19, Target disclosed that as many 40 million credit and debit cards were compromised between Nov. 27 and Dec. 15 by malware installed on the company's point of sale registers.
(Read more: Target CEO defends delay to disclose data breach)
Target said Friday its continuing investigation found that at least 70 million customers' personal information was stolen from its database—including names, mailing addresses, telephone numbers, and email addresses. The retailer expects some overlap in the two data sets but does not have the exact numbers yet.
Also Friday, Neiman Marcus disclosed that some its customers' credit cards were compromised in a security breach.