It is the iconic green space of New York City, internationally renowned and beloved by generations of natives and visitors alike.

Yet for Mayor Bill de Blasio, Central Park and its emerald fields have morphed into something else: an improbable political battleground.

The mayor’s plan to ban horse-drawn carriages, an obscure proposal until Mr. de Blasio embraced it in last year’s mayoral race, has erupted into a cause célèbre, landing on the cover of The New Yorker and dominating local headlines, even as Mr. de Blasio is trying to refocus his administration on housing and wage issues.

International celebrities and federal investigators are swooping in. Nicolas Sarkozy, the former French president, said in New York this week that he wanted the horses to stay. The Federal Bureau of Investigation is looking into a political group that worked with animal-rights lobbyists to support Mr. de Blasio’s candidacy, The Daily News reported on Friday.