Earlier, the mayor said the matter needed more study but now Bloomberg says, "The public is overwhelmingly in favor" of the ban, The New York Daily News reported Thursday.
Bloomberg initially hedged when Health Commissioner Thomas Farley proposed the smoking ban last month, saying enforcement would be difficult.
Controller William Thompson, Bloomberg's political opponent, said he also would pursue the ban if elected.
Rosie O'Donnell unveils nearly 50-pound weight loss
Iranian woman stops the execution of son's killer