Elected to lead the biggest city in the nation, Mayor Bill de Blasio often seems to hunger for a brighter spotlight. He tried to shape the debate in the last presidential election, only to be spurned by candidates in his own party. He flew to Germany in July to speak at a rally during a meeting of world leaders, only to be criticized for leaving New York hours after a police officer was murdered.

Now he has seized hold of the national debate over the removal of confederate monuments by ordering a review of all possible “symbols of hate” in the city — once again grabbing national attention while simultaneously putting himself in a tricky situation.

He has been peppered with questions about how far the review will go to cleanse New York of potentially offensive figures and whether this or that sculpture should stand or fall. Some see him as playing into the hands of President Donald J. Trump, who warned that the push to remove Confederate monuments could go too far.

“He’s going to create some kind of star chamber to see who’s politically correct and who’s not,” said Kenneth T. Jackson, a historian who edited The Encyclopedia of New York City, echoing other historians who have cautioned against the rush to remove statues and monuments.