More than 1.2 million people have signed a pledge to boycott Target after it announced last month that it would welcome transgender customers to use any bathroom or fitting room that matches their gender identity.
The backers of the pledge - including Texas Lt. Gov. Dan Patrick - claim that the policy poses a "danger to wives and daughters" and is "exactly how sexual predators get access to their victims."
In an interview on CNBC on Wednesday, Cornell said he continues to believe that Target made the right decision in supporting transgender rights.
"We took a stance and we are going to continue to embrace our belief of diversity and inclusion," Cornell said.
He reassured customers who are concerned about their safety, saying, "we are also going to make sure our commitment to safety is unwavering."
Cornell likened the public backlash against Target to when the retailer started used African American models in advertising in the mid 1960s.
"Back then it wasn't well received, but sitting here today we know we made the right decision," Cornell said.
Cornell also noted that a majority of Target's stores already have a family restroom and "we are committed over the next few months to make sure every one of our stores has that option because we want all our guests to be welcomed in our stores."