Wells Fargo has repeatedly promised to take steps to compensate customers who had accounts opened in their names without their knowledge. But four months after admitting to the sham accounts, the San Francisco bank still refuses to say how many of its hometown customers were victims.

On Tuesday, City Treasurer Jose Cisneros sent a letter to Wells Fargo demanding it disclose how many San Francisco residents had credit card and bank accounts opened without their knowledge — information Cisneros said he first asked for in September. He also wants to know what the bank will do to repay those customers, some of whom were charged fees by Wells Fargo on the accounts they didn’t know they had.

In addition, Cisneros demanded that the bank disclose how many “low-level employees” in San Francisco were fired for opening the accounts under what he called “great pressure to do whatever it took to meet aggressive sales goals,” and how the bank will repair the damage to their careers.

“Wells Fargo has the answers to all of this. ... They certainly know where those people live,” Cisneros said in an interview. “You kind of got to fess up for us to start to build trust again, and to the degree that you don’t come out with the whole truth, how can I know when it’s time to trust again?”

The treasurer is the banker, tax collector, collection agent and investment officer for the city, and he wields some control over how much business San Francisco does with Wells Fargo. Cisneros terminated the bank’s brokerage dealings with the city shortly after the scandal broke in September and also kicked Wells Fargo out of the city’s Bank On program, which helps low-income residents start bank accounts.

But the city could take further steps, such as refusing to let Wells Fargo underwrite any of its bonds, which are worth billions of dollars.

Ruben Pulido, a spokesman for Wells Fargo, said, “Stakeholders are asking us many legitimate questions,” but that “unfortunately, we cannot answer some questions at this time due to an ongoing internal review.”

Regulators say Wells Fargo opened about 2 million unauthorized accounts nationwide. Pulido said the bank has refunded $2.6 million to customers nationally.

Cisneros isn’t the only San Francisco official losing patience with Wells Fargo. On Tuesday, the Board of Supervisors unanimously passed a resolution urging the district attorney to investigate Wells Fargo executives and calling on the San Francisco Retirement Board to terminate all financial dealings with the bank. It also endorsed the city controller’s decision to pull $4.5 million in city funds from Wells Fargo short-term checking accounts, among other measures.

There were several connections the board didn’t touch, however, and those illustrate how hard it would be for the city to disentangle itself from Wells Fargo completely. For example, the bank will continue to serve as a credit provider for about $200 million worth of bonds issued by San Francisco International Airport, a $160 million issue for the Transbay Transit Center project and $75 million for the city Public Utilities Commission.

“They have their tendrils in all parts of our society, including the city and county of San Francisco, so in a way we are tied to their success or failure,” said Supervisor John Avalos, who sponsored the resolution.

But even if San Francisco’s actions are more symbolic than a financial threat to a bank with more than $1.7 trillion in assets, it’s incumbent on the city to do what it can, Avalos said.

“If we don’t practice our power as a city to force better behavior and standards of business, then what good are we doing to protect the public?” he said.

Edward Mills, a financial policy analyst at FBR Capital Markets in Washington, D.C., said government agencies have to balance competing interests if they want to punish banks with which they do business.

“That’s the challenge — the desire to inflict some sort of penalty with the desire to still have a functioning banking system that we use to operate our daily lives,” Mills said. “The worst way you can take out your animus toward one of the big banks is causing higher financing costs that cause you to cut the position of a fireman or a teacher.”

He said there is little San Francisco could do to hurt Wells Fargo’s bottom line. “You’re not going to impact their revenue. You’re going to impact the way Wall Street views their stock price. And that affects the value of their company,” Mills said.

But Peter Conti-Brown, an assistant professor of legal studies and business ethics at the University of Pennsylvania’s Wharton School, questioned the city’s decision not to sever more ties with the bank.

“It’s not enough to say it’s cheaper to do business with Wells Fargo, because that includes the cost of linking the city’s reputation with an organization that has admitted to defrauding its customers,” Conti-Brown said. “How do you quantify the cost of that reputational uncertainty?”

In recent days, Wells Fargo’s sales scandal has widened to include revelations that bank employees may have opened Prudential life insurance policies for customers who didn’t ask for them. A whistle-blower lawsuit filed by three former Prudential employees said the bank opened many such accounts for customers who didn’t speak English.

Wells Fargo has sought to squelch customer lawsuits over sham accounts by forcing the plaintiffs into arbitration — a venue that plaintiffs’ lawyers say can be tilted toward corporate defendants. The bank has argued that although the accounts were unauthorized, the victimized customers agreed to submit any disputes to arbitration when they opened legitimate accounts.

“That’s the definition of chutzpah as far as legal procedures go,” Conti-Brown said. “One reason (Wells Fargo) hasn’t come fully clean and released a top-to-bottom investigation of this is they face real liability risk if they do so.”

In going to war with Wells Fargo, the city could also jeopardize bank support for civic institutions. The bank is one of the city’s largest donors, giving about $30 million to San Francisco organizations from 2013 to 2015. Since 2000, it has donated more than $4 million to Glide Memorial United Methodist Church in the Tenderloin and $2 million to San Francisco General Hospital, according to the Wells Fargo Foundation.

Jim Wunderman, president and CEO of the Bay Area Council, a public policy group representing many of the region’s largest companies, expressed support for the bank.

“We’re not apologists for Wells Fargo, nor would we ever condone the types of illegal banking activities in which the bank engaged,” he said. “But we do think it’s only fair that people also have some awareness of how much good Wells Fargo has done for San Francisco, residents, businesses, public agencies and the region.”

Emily Green is a San Francisco Chronicle staff writer. Email: egreen@sfchronicle.com Twitter: @emilytgreen