Mr. Rossman is head of a unit at Lazard that helps companies fend off attacks on management by hedge funds and other activist investors. He told reporters this month that the activist funds, often with the quiet support of big mutual funds, had lately been targeting European companies, demanding changes that they think will deliver a bigger payoff for shareholders.

The possibility of a no-confidence vote rose after shareholder advisory firms urged investors to send a message.

“We believe it is time for shareholders to hold the boards accountable for the many years of substantial monetary and reputational costs to the bank borne by shareholders,” one of the firms, Institutional Shareholder Services, said in a report this month that advised clients to vote against ratifying Deutsche Bank’s management and supervisory boards.

ISS and Glass, Lewis & Company, another influential advisory firm advocating a vote of no confidence, cited the damage inflicted on the bank’s finances and reputation by persistent money-laundering scandals.

On Wednesday, Deutsche Bank acknowledged that it had used faulty software to screen customer transactions for suspicious activity. The bank said it had alerted regulators and was working to fix the problem as soon as possible.

Mr. Sewing, the chief executive, promised Thursday to improve the bank’s internal controls. But he also suggested that the bank was unfairly targeted when German prosecutors raided company offices in Frankfurt in November as part of a money-laundering investigation. The negative media coverage “hit us hard,” Mr. Sewing told shareholders.

“It is, of course, a criminal investigator’s duty to conduct a thorough examination of any suspicious circumstance,” he said. “However, it’s possible to have diverging views on the manner in which it happened in November.”