Allegations of widespread bribery at Wal-Mart’s Mexican subsidiary continued to reverberate on Tuesday, with the company beginning a campaign to limit the damage as its shares declined further.


In a statement, Wal-Mart said it had beefed up its internal controls to make sure it was complying with the Foreign Corrupt Practices Act, which prohibits American companies from bribing foreign officials to secure business. In a newly created position, a top-level compliance official will be responsible for ensuring that the company abides by the law and will oversee five regional compliance directors based in international markets.


In Mexico, the retailer said it had bolstered its training, auditing and internal controls to ensure better compliance with laws against bribery.


“We are taking a deep look at our policies and procedures in every country in which we operate,” said David Tovar, a Wal-Mart spokesman.


The New York Times disclosed on Sunday that Wal-Mart’s own investigators had found evidence that Wal-Mart de Mexico had paid millions of dollars in bribes to help advance its expansion in a crucial market. When executives at Wal-Mart’s Arkansas headquarters were told of the findings, they shut down the investigation, The Times found.


But on Tuesday, Mr. Tovar shot back, “We believe it’s also important to keep a few things in context: The allegations in the New York Times story about the decisions made in Bentonville are more than six years old.” In addition, he noted that Wal-Mart began its own investigation six months ago and was cooperating with law enforcement authorities.


Shares of Wal-Mart, the world’s largest retailer, fell an additional 3 percent on Tuesday, after a 5 percent decline on Monday, closing at $57.77. Shares of Wal-Mart de Mexico, which trades separately, fell 4 percent Tuesday, after a 12 percent decline on Monday.


In a related matter on Tuesday, one of the executives identified in the Times article as a driving force behind the bribery in Mexico, Eduardo Castro-Wright, announced that he had resigned from the board of MetLife, on which he had served since 2008. Mr. Castro-Wright was promoted to vice chairman of Wal-Mart in 2008 and is scheduled to retire this summer.


“Over the past weekend, I notified you of recent events that will require my immediate and personal attention,” he said in his letter of resignation, adding later, “I now must focus my energy in spending personal time with my family and in protecting my good name and business reputation.”


MetLife officials declined to comment further on the resignation.


In late 2011 the Justice Department opened a Foreign Corrupt Practices Act investigation into Wal-Mart — apparently after the corporation had learned of The Times’s reporting and disclosed the problems to the government. Wal-Mart said at the time that it was conducting an internal inquiry, a person with knowledge of the matter confirmed.


While the inquiry continues, it is not clear to what extent the case is being actively investigated by federal agents. In cases in which the evidence is overseas and corporations have a strong legal incentive to cooperate with the government to avoid indictment, the work of assembling the facts is often performed largely by counsel retained by the corporation.


In a statement over the weekend, Wal-Mart said that it had continued to meet with federal officials to “report on the progress” of its internal inquiry.


The Times article prompted calls for outside investigations in both the United States and Mexico, as well as angry protests from union leaders and activist groups that have long been critical of the retailer’s practices.


On Monday, two Democratic representatives, Elijah E. Cummings, of Maryland, and Henry A. Waxman, of California, said they had requested a meeting with Wal-Mart officials and others who might be familiar with the bribery allegations. But Representative Darrell Issa, the Republican chairman of the House oversight committee, appeared to shoot down the idea of Congressional hearings.


“In the case of Wal-Mart, they will be punished under existing laws,” he said Tuesday in an interview on Bloomberg Television. “As we review Wal-Mart, it has to be to look at government’s role, not simply hauling people in because it makes good headlines.”


A similar dynamic was playing out in Mexico, as candidates for the presidency called for an investigation, while the government said it was a matter better left to state and local authorities.


A spokesman for Enrique Peña Nieto, the front-runner in the Mexican presidential race, set to vote July 1, said the candidate was in favor of a government investigation of the allegations against Wal-Mart, echoing lawmakers from his party.


Another major party candidate, Andrés Manuel López Obrador, who has often criticized Wal-Mart’s practices, said Sunday that the case showed the government was “rotten.”


But late Monday night, the Mexican Economy Ministry issued a statement saying that the Wal-Mart allegations referred to permits and licenses obtained at the municipal and state level, outside federal jurisdiction, and did not indicate involvement of federal officials.


“The federal government does not have province in the matters which the investigation alludes to,” the statement said.


Government officials have generally lavished praise on Wal-Mart, now Mexico’s largest private employer and retailer with more than 2,000 stores and restaurants. Just a few weeks ago President Felipe Calderón, after meeting with its chief executive, celebrated its clean energy goals in its stores and its contributions to the economy, including a promised 23,000 new jobs, although labor groups have complained about its wages and the placement of a subsidiary store near archaeological ruins.


Mr. Calderón’s office had no comment.