Bloomberg is calling for the city to establish a minimum price of $10.50 for a pack of cigarettes or small cigars.
The mayor says that will make smoking too expensive to lure in teenagers or the poor.
The bill, a companion to Bloomberg's plan to move cigarettes out of sight in stores, would also prohibit retailers from redeeming coupons or offering other discounts like two-for-one deals
Providence, Rhode Island, started a similar policy in January.
Tobacco companies sued, but they lost. They are now appealing.