“Mayor Emanuel believes this is an architecturally tasteful building scarred by an architecturally tasteless sign,” Kelley Quinn, the mayor’s spokeswoman, said in a statement on Thursday. She acknowledged that the sign had been approved by the City Council last year, but said that Mr. Emanuel had instructed Mr. Trump’s office to determine any “options available for further changes.”

The building, the Trump International Hotel & Tower, was once intended to be the tallest building in Chicago, surpassing the Willis Tower, an ambition that was eventually scaled back to its current 1,392-foot form. The building, designed by the Chicago architect Adrian Smith, replaced a squat Chicago Sun-Times building with aging yellow lettering.

The 12th-tallest building in the world, the tower was constructed of 30 miles’ worth of glass that rockets into the sky, surrounded by some of Chicago’s most famous architectural accomplishments. On one side sits the historic Wrigley Building and Tribune Tower; on the other is the corncob-shaped Marina City.

“Look at all these buildings; none of them have names on them,” said Cole O’Beirne, 25, who works for a company that gives kayak tours of the city’s architecture. He said it was only a matter of time before Mr. Trump brought his self-promotional style to Chicago, a Midwestern metropolis that shies away from such East Coast swagger.

“It’s very New York,” he said about the Trump sign. “It’s very flashy.”

Mr. Trump has robustly defended his decision, calling the sign popular among his fans and good for Chicago’s image.