LONDON — Barclays shareholders vented their frustrations with James E. Staley, the British bank’s chief executive, on Wednesday after he was caught up in a regulatory inquiry last month over his treatment of a whistle-blower complaint.

At the bank’s annual meeting in London, one shareholder called for Staley to step down from the stage — John McFarlane, the Barclays chairman, declined the request — and another later asked for Staley to resign immediately.

On Wednesday, Staley offered another in a series of public apologies for his actions.

“I feel it is important that I acknowledge to you — our shareholders — that I made a mistake in becoming involved in an issue which I should have left to the business to deal with,’’ Staley told investors Wednesday. “I have apologized to the board, and I would today like to apologize to you as well, for that error.’’

Meanwhile, Barclays will pay $97 million to settle charges that it overbilled some of its advisory and brokerage clients.

The US Securities and Exchange Commission said Wednesday that affected clients will get a refund.

In its complaint, the SEC said more than 2,000 accounts were charged about $48 million in fees for a service that Barclays did not provide and more than 22,000 accounts were charged about $2 million in excess fees. The complaint also said that Barclays steered some clients with brokerage accounts toward expensive mutual funds when cheaper funds were available.

The overbilling occurred between 2010 and 2015 at Barclays’ wealth and investment management business, which it sold at the end of 2015, the regulator said.

In settling, the SEC said that Barclays did not admit or deny its findings.

Barclays PLC declined to comment.

British regulators are investigating Staley after he sought to learn the identity of a whistle-blower last year after the company received two anonymous letters that involved a former colleague at JPMorgan Chase whom he had hired.

The bank has previously said it would formally reprimand Staley, who is known as Jes, and make a “very significant compensation adjustment’’ to his bonus after investigators completed their work.

McFarlane said that Staley mistakenly believed at the time that the matter was closed and he could proceed with efforts to learn the individual’s identity. McFarlane said Staley only wanted to contact the individual to get him or her to stop writing letters, because he believed they were malicious.

“He thought he had a green light. He went through the green light and it was actually red,’’ McFarlane said. “The action for going through a red light is usually you do not lose your license.’’

The disclosure of the inquiry prompted Institutional Shareholder Services, the influential proxy adviser, to recommend last month that investors withhold their votes for his re-election to the board.

Staley was re-elected to the board Wednesday, receiving 97.2 percent of the votes cast. Votes representing about 1.7 billion shares were withheld.

McFarlane dismissed the call for Staley’s resignation, noting the bank’s prospects have improved under his leadership.

“If I believed a chief executive should go, you know me, he would go,’’ McFarlane said.

In addition to the British regulators — the Financial Conduct Authority and the Prudential Regulatory Authority — the New York Department of Financial Services is looking into the matter.

The inquiry has emerged at a pivotal time for Barclays, which has large operations in New York and in London. Staley is the bank’s third chief executive after it was caught up in a scandal involving the manipulation of a key benchmark interest rate, the London interbank offered rate, or Libor.

Barclays paid $450 million in penalties and became the first bank to admit to wrongdoing in 2012 related to Libor, with the resulting scandal costing Robert E. Diamond Jr. his job. Antony Jenkins was brought in to change the bank’s culture, but he was ousted two years ago after directors lost faith in his ability to turn around the company.

Staley joined the bank in December 2015 and has moved aggressively to sell off businesses the bank does not consider core operations in the future and resolve legacy misconduct issues that have dragged on its results.

In February, the British bank said that it was on the verge of closing a unit that houses its noncore operations and would no longer be in a restructuring mode by later this year.

Material from the Associated Press was used in this report.