The advocacy groups focused on JPMorgan in part because it is the city’s biggest bank.

A spokesman for the bank said that Chase Liquid, a prepaid card, “has helped more than a million people gain access to mainstream banking.”

The municipal ID cards are available to all New Yorkers over the age of 14. While the mayor’s office says it cannot track the exact number of immigrants with the cards, it has seen some encouraging signs. In the Corona Park neighborhood of Queens, for example, about 20 percent of the area’s approximately 150,000 residents have the cards, according to the mayor’s office.

Late Wednesday afternoon, at an unrelated event in Brooklyn, the mayor defended the ID card program, saying the cards were being accepted by many banks, credit unions and other organizations and have “had a big impact on everything else in people’s lives, whether it is going for a lease, going for a library card, getting into their child’s school when they have to show an ID.”

As for the banks that have declined to accept the card, the mayor said: “We’re certainly going to talk to them, and we’re certainly going to help them to understand.” He expressed confidence that the banks’ concerns could be overcome.

Image A sample of the New York identification cards known as IDNYC.

“I think we can educate these banks about the fact that it is both an extraordinarily accurate ID, but it’s the right thing to do for New York City.”

The mayor emphasized that the cards were developed with input from the New York City Police Department and said the department had been one of the biggest backers of the program. “They want every New Yorker on the street to have an ID card; it greatly improves the work of the NYPD,” Mr. de Blasio said.