The fruitless 2005 discussions re-emerged as an issue for John C. Liu, the New York City comptroller who is the trustee of the pension funds, because that was the year high-level Wal-Mart officials were told of bribery in its Mexico unit, according to a recent report in The New York Times. It is unclear whether Wal-Mart’s independent directors were aware of the Mexican improprieties, which The Times reported were related to expediting government approvals to build stores.

“In its relentless drive for profit and expansion, Wal-Mart has paid millions to settle charges that it violated child labor laws and exploited immigrants,” Mr. Liu said Monday, in announcing the decision to vote against the company’s directors. “Now we learn that not only did Wal-Mart allegedly bribe its way through Mexico, but may have tried to cover up the corruption. A select few Wal-Mart executives may benefit in the short term, but the company, its share owners and everyone else lose in the long run.”

Wal-Mart declined to comment.

The directors opposed by the New York City pension funds are Michael T. Duke, the company’s chief executive, and H. Lee Scott Jr., his predecessor. Pension fund officials said in a statement that Wal-Mart’s failure to pursue an independent investigation into bribery allegations in 2005 “has potentially exposed the corporation and its share owners to even more serious financial and reputational harm.”

Along with opposing corporate insiders, the shareholders will vote against Christopher J. Williams, chief executive of the Williams Capital Group, an investment bank, who heads the audit committee of the Wal-Mart board and who has been a director since 2004; and Arne M. Sorenson, the chief executive of Marriott International, who sits on the audit committee. They will also oppose the board chairman, S. Robson Walton, because he presides over a board consisting of too many directors with company ties, Mr. Liu said.