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The accusations read like a pulp thriller: Citigroup employees in Mexico are suspected of pocketing millions of dollars in kickbacks from vendors. And bodyguards for bank executives bought audio recordings of personal phone calls and created shell companies to disguise their fraud.

A new scandal has erupted at Citigroup’s Mexican unit just months after a $400 million fraud involving a well-connected client. Now the sprawling global bank — which separately announced plans on Tuesday to withdraw from consumer banking in 11 other markets — is wrestling with how to get its house in order in one of its oldest foreign operations. A crucial part of that decision rests on how to nudge aside the most powerful executive overseeing Mexico, a country where Citigroup has been doing business since 1929.

What makes that decision particularly difficult is that the Mexican unit, Banamex, mints money. Still, the scandals at Banamex — and the investigations in two countries that have come as a result — have exposed the bank to risk at a time when Citigroup is trying to reduce its legal and regulatory burdens.

In a delicate dance, Citigroup is encouraging its Mexico chairman, Manuel Medina-Mora, 64, to retire, according to four people briefed on the matter. The bank has been quietly laying the groundwork for his departure, which could come by early next year, the people said.

Still, Mr. Medina-Mora’s business acumen and connections to the country’s ruling elite have made him critical to the bank’s success in Mexico. Citigroup and its chairman, Michael E. O’Neill, cannot afford to alienate Mr. Medina-Mora and risk jeopardizing those relationships, these people said. But the latest problems uncovered at Banamex are augmenting concerns about lax controls and oversight in Mexico.

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In particular, Mr. O’Neill has privately expressed concerns to board members that Mr. Medina-Mora, who is also co-president of the parent company, has not always relayed problems in the region to executives at the bank’s headquarters on Park Avenue, according to the people briefed on the matter. Instead of looping in executives in New York, Mr. Medina-Mora has at times chosen to handle the issues himself.

Mr. O’Neill and Citigroup’s chief executive, Michael L. Corbat, respect Mr. Medina-Mora’s long track record overseeing Banamex, which has reported strong, consistent profits under his stewardship, according to two people close to the bank executives. The timing for a change might be right for Mr. Medina-Mora, who commutes between New York and Mexico, where his family is. He has told colleagues that he has long wanted to retire by age 65, these people said.

In a statement on Tuesday, when the bank also released its third-quarter results, the Citigroup spokesman Mark Costiglio said: “Manuel Medina-Mora is a highly valued and well-respected member of the management team who has an outstanding track record globally in consumer banking, as today’s results show.”

The gentle handling of an exit for the Mexican chieftain contrasts with a startling boardroom coup nearly two years ago when Mr. O’Neill led the ouster of Vikram S. Pandit, who had steered the bank through some of its darkest days, as chief executive.

It has been a rocky year for Banamex. In February, Banamex disclosed a $400 million fraud involving the politically connected, but financially troubled, oil services firm Oceanografía.

The latest scandal at Banamex centers on the bank’s security unit. An internal investigation, begun by Citigroup in July, found evidence that the security unit was overcharging vendors and may have been taking kickbacks, a person briefed on the investigation said. The internal inquiry also found shell companies that had been set up to look like vendors and receive payments from the Banamex unit.

The security unit was created in 1994, after a former Banamex president had been kidnapped and held for ransom by a guerrilla group. It remained intact after Citigroup acquired Banamex in 2001.

The security unit’s primary purpose was to protect the Banamex leadership, but at some point, the unit started operating beyond its approved duties, according to the person briefed on the matter who was not authorized to speak publicly because of the criminal investigation. The security unit was also providing protection and security consulting services for people outside the bank, sometimes as a courtesy and at other times for money, the internal investigation found. The conduct spanned more than a decade, the investigation found, extending into last year.

The unit, which Citigroup disbanded in light of the investigation, was run by Federico Ponce Rojas, a former official with the Mexican attorney general’s office who resigned from Banamex in December. Mr. Ponce did not respond to requests for comment.

His exit was followed a few months later by the departure of Banamex’s chief executive, Javier Arrigunaga, a 12-year veteran of Banamex’s management team. There was no evidence that the fraud reached executives.

Even so, in a statement on Tuesday, Mr. Corbat called the conduct of individuals in the security unit “appalling.”

Citigroup’s outside lawyers have turned over information to law enforcement officials in Mexico and the United States, but there are many things the bank doesn’t know about the rogue security unit. For example, the security team had purchased audio surveillance files from “third parties” that included cellphone and landline conversations of dozens of people — some of a highly personal nature, the person said. The Banamex unit then transcribed many of these files. It was unclear why the security team was amassing records of the personal conversations. The bank’s investigators are still working to determine why the security unit gathered the conversations, involving dozens of people, many of whom had nothing to do with the bank.

And despite the latest headline-grabbing turmoil at Banamex, Citigroup does not want to cede any ground in Mexico where it dominates a large portion of the retail market.

In other less profitable parts of the world, Citigroup is retreating. On Tuesday, the bank announced that it was selling its consumer business in 11 markets, across Latin America, Asia and Europe.

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The plan to cast off the international consumer businesses is expected to be completed by the end of 2015. The sales represents another milestone for the sprawling global bank.

Since the financial crisis, Citigroup executives have been trying to winnow the bank’s business lines and hone its strategy to focus on investment banking and more affluent consumers, particularly in the United States. That effort to simplify its operations gained urgency earlier this year after the Federal Reserve rejected the bank’s capital plan, citing concerns about its projections for potential losses in “material parts” of its global operations.

The latest fraud investigation in Mexico marred otherwise positive third-quarter results, which the bank also announced on Tuesday. Citigroup said its profit increased 13 percent from the period a year earlier, as trading picked up and credit losses continued to decline.

The bank reported profit of $1.15 a share on revenue of $19.97 billion, adjusting for one-time items. Wall Street analysts surveyed by Thomson Reuters expected adjusted net income of $1.12 a share and revenue of $19.05 billion.

Elisabeth Malkin and Ben Protess contributed reporting.