Mr. Kennedy said he planned to file complaints with the Consumer Financial Protection Bureau against banks that are effectively restricting gun sales by setting their own rules on legal products and refusing to do business with gun makers and retailers that do not comply. He is also working to get Republican colleagues to join him in writing legislation to stop banks from discriminating against gun buyers.

Major banks have taken a series of steps this year to prevent guns from falling into the wrong hands. They are restricting their credit card and banking services to gun retailers and halting lending to gun makers that do not comply with age limits and background check rules determined by the banks. They are also freezing out businesses that sell high-capacity magazines and “bump stocks,” attachments that enable semiautomatic rifles to fire faster, even though such products are legal under federal law.

Citigroup was the first to unveil such a firearms policy in March when it announced that it would forbid any new retail clients who operate gun shops to sell guns to people who have not passed background checks. It also restricts those shops from selling firearms to people younger than 21 and bars sales of bump stocks and high-capacity magazines. Gun sellers that do not comply will not be able to raise capital through Citigroup, and the bank said it would look to move away from existing clients that do not change their policies.

In April, Bank of America said it would no longer lend money to manufacturers of military-inspired firearms that civilians can use, such as AR-15-style rifles. A bank executive said the policy was intended to help reduce mass shootings.

BlackRock, the world’s largest asset manager, said it would begin offering a new line of investment funds that do not include producers of firearms or retailers that sell them, cutting off a potential avenue of financing for gun makers and retailers.