In the weeks since the Parkland shootings, I’ve had conversations with dozens of chief executives and other leaders from a variety of industries, many reaching out directly about the internal debates they have had. Virtually all the major banks, JPMorgan Chase and Bank of America among them, have created formal or informal working groups to consider the issue, as have the big credit card companies, including Visa, Mastercard and American Express.

(Perhaps the bank that’s least receptive to addressing the issue of guns is Wells Fargo, which has said it should be approached through the “political and legislative process.” Wells Fargo is the largest financier in the nation of the gun industry and is the main bank for the National Rifle Association, according to Bloomberg.)

With the exception of Citi, most financial institutions are still grappling with how to properly carry out a plan that is both enforceable and does not encroach on the rights of its customers.

While Citi’s decision is significant, Mr. Corbat acknowledged that it was intended to be balanced — and he purposely didn’t want it to be too broad. “This isn’t an easy thing to simply take a stance on,” he said, because of various privacy laws and rights.

“There is an important nuance here,” he said. “We didn’t tell our hundred and sixty million card holders in the world how they can use their cards. It’s their money. But what we did say — in terms of the people that Citi is going to do business with, the ones that we’re going to finance and that we’re going to, in essence, put our brands together on — that there needs to be something that makes sense for us and for both sides.”

He said the bank had purposely left some of its policy ambiguous so it could accommodate potential exceptions — for example, to the 21-year-old age limit.

“My inbox lit up with people saying: ‘Dear Sir, I’ve served in the military. Our country gave me a firearm when I was 18, and it was fine for me to go use that in the defense of our country,’” Mr. Corbat said.