He added: “There is already a mosque four blocks away. Should it, too, be moved? This is a test of our commitment to American values. We must have the courage of our convictions. We must do what is right, not what is easy.”

It was Mr. Bloomberg’s second major speech in three weeks supporting the plan, and its soaring tone and forceful arguments suggested that he had firmly embraced his role as a national defender of the plan for the center, even as high-profile voices have called for a re-examination of the wisdom of the current site.

Mr. Bloomberg rejected those calls, arguing that to move the center would slight American Muslims and damage the country’s standing.

“We would send a signal around the world,” he said, “that Muslim Americans may be equal in the eyes of the law, but separate in the eyes of their countrymen. And we would hand a valuable propaganda tool to terrorist recruiters, who spread the fallacy that America is at war with Islam.”

As the controversy has snowballed, the families of some Sept. 11 victims have lashed out at Mr. Bloomberg for supporting the project, saying he has lacked sensitivity to their pain.

The mayor seemed to directly address that criticism on Tuesday night. “There will always be a hole in our hearts for the men and women who perished that day,” he said, at one point acknowledging a woman in the room named Talat Hamdani, a Muslim whose son, Salman, was killed on Sept. 11.

But as he has in the past, with a mixture of compassion and impatience, Mr. Bloomberg encouraged the families of those who died to move on emotionally. New Yorkers, he said, had collectively rejected calls to make the entire World Trade Center grounds a memorial.