Wal-Mart Stores Inc. won the right to open two more stores in Chicago this year, but does that mean the world’s largest retailer can eventually take Manhattan?

In remarks at the start of a two-day analyst meeting, Leslie Dach, Wal-Mart’s executive vice president for government affairs and corporate relations, said the retailer’s reputation has shown improvement with both consumers and elected officials.

The improvement for Wal-Mart, which has long been a target for critics that complained about the level of pay and benefits it offered employees, its impact on competitors and other issues, has made it easier for the company to win approval for new stores, Dach said.

Wal-Mart won Chicago City Council approval this summer to open two new stores in the city after satisfying a key union group’s concerns over wages.

Dach was introduced by the Wal-Mart Associates Choir singing “My Kind of Town,” the tribute to Chicago made popular by Frank Sinatra.

His presentation ended with the choir singing another Sinatra staple, “New York, New York,” an apparent tongue-in-cheek nod to speculation of where Wal-Mart might want to eventually expand as it looks to bring more stores to densely populated urban areas in search of sales growth.

Wal-Mart has no stores in New York City, while rival discounter Target Corp. penetrated the Manhattan market with a store in Harlem earlier this year after 13 years of trying to open the site.

Dach followed up the singing of New York, New York with a disclaimer.

“Any relationship between our choice of songs and any actual political strategy is purely fictional,” he said.

But Dach did list bringing more stores to urban markets as one of the immediate issues for the company.

Dach said the company learned a lot in Chicago, but conceded that different markets had different political dynamics.

“We know all politics is local in this country and we will have to fight that fight wherever we go,” Dach said.