The city comptroller, William Thompson, is stepping up his criticism of Wal-Mart with a demand that the world’s largest retailer turn over company records to his office.

The custodian of the five major public pension funds for the city, the comptroller sent a letter to Wal-Mart last week asking for files relating to a potentially illegal surveillance of shareholders by the company, the comptroller’s office announced yesterday.

Coming from a likely mayoral candidate in 2009, the move adds to a list of New York City-related frustrations for Wal-Mart, as residents, elected officials, and unions have fought back the company’s repeated attempts to build a store within the five boroughs.

Mr. Thompson has been critical of the corporation since an April 4 article in the Wall Street Journal reported that Wal-Mart was investigating potential opponents and certain shareholders prior to a board meeting, though the company has denied any wrongdoing.

Earlier this year, Mr. Thompson urged the Securities and Exchange Commission and the state attorney general’s office to examine the matter, though in requesting the documents, the comptroller appears to be initiating an investigation of his own.

In the letter, Mr. Thompson told Wal-Mart that he has a credible basis to think members of the company “have improperly expended corporate assets in connection with conducting surveillance of proponents of shareholder proposals.”

A spokesman for Wal-Mart, John Simley, said the company is reviewing the request and intends to reply. “We’ve just received the letter, so we’re studying it and we’ll respond appropriately,” he said.

Wal-Mart has rejected assertions that the company has engaged in illegal surveillance activities.

The attacks by Mr. Thompson come as the retailing giant, despite claiming more than 3,500 stores in America, has yet to crack into the New York City marketplace.

A lobbyist with a retail organization that opposes Wal-Mart, Richard Lipsky, said the company’s efforts are likely to fail with the existing City Council.

“They were unable to navigate Cottonville in Staten Island because of local opposition in the most conservative district in the city,” Mr. Lipsky said. “It’s hard to see them overcoming that in other neighborhoods of the city.”

A senior fellow at the Manhattan Institute who is a proponent of Wal-Mart stores, Steven Malanga, said it is often politically expedient for New York City politicians to criticize the company.

“It seems to play well if you can find a way to attack the giant that Wal-Mart has become, so everybody winds up to take their whacks,” Mr. Malanga said.

A spokesman for Mr. Thompson did not return a request for comment.