The statement came on the same day of a concerted effort by business leaders to influence the gun debate. In a letter on Thursday, the heads of 145 companies in the United States — including Twitter, Uber, Levi Strauss, Amalgamated Bank and Dick’s Sporting Goods — urged Senate leaders to consider an expansion of background checks and stronger “red flag” laws.

Mr. O’Rourke’s plan was informed by a New York Times investigation last year that reviewed police reports, bank records and investigator notes from a decade of mass shootings and found that many of the killers had used credit to stockpile high-powered weapons.

In response to that reporting, some banks and credit card networks said that customers were entitled to privacy and independence, and that it was not the companies’ responsibility to create systems to track gun purchases that would allow them to report suspicious patterns.

Several bank and credit card companies did not respond to requests for comment on Thursday. Visa did not comment on Mr. O’Rourke’s proposal, but said in a statement that it agreed with the 145 companies that had called on Congress to advance gun control legislation such as expanding background checks and implementing “red flag” laws.

Some banks have revised their policies in recent years. Citigroup said in March 2018 that it would work only with clients that agreed to certain restrictions on firearm sales, and Bank of America said in April 2018 that it would stop lending money to gun manufacturers that make military-inspired firearms for civilian use.