Mayor Bill de Blasio is pushing legislation to hike New York City’s minimum cigarette-pack price to $13, halve the number of stores allowed to sell tobacco products and put pharmacies out of the tobacco business altogether.

Speaking Wednesday at the American Heart Association’s offices in Manhattan, de Blasio said he hopes to sign five anti-tobacco bills this year, toward a larger effort to cut the number of smokers in the city by 120,000 from the current 900,000 by 2020.

One of the bills, sponsored by Councilman Corey Johnson (D-Manhattan), raises the minimum per-pack price of cigarettes from $10.50 to $13. Because of idiosyncrasies in state law regulating the city’s taxing powers, the retailer, not the city, would pocket the difference.

Johnson’s bill also would levy a 10 percent tax on other tobacco products, such as shisha containing tobacco, loose tobacco, smokeless tobacco and cigars. That revenue, expected to be about $1 million, under state law would have to go to benefit public housing.

Another bill, by Councilman Brad Lander (D-Brooklyn), would prohibit pharmacies, or stores that contain pharmacies, from selling tobacco products. There are more than 550 such pharmacies in the city with tobacco-selling licenses.

Lander also sponsored a bill that would eventually cut the number of retailers allowed to sell tobacco by half in each community district. No current tobacco retailer would lose its license under the bill, but no new ones would be issued until the district’s number is below the cap.

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A store owner who sells the business would be able to transfer the license and be unaffected by the cap, said Lorelei Salas, commissioner of the Department of Consumer Affairs.

The other bills would create a new e-cigarette license and require residential buildings to create a smoking policy.

A tobacco industry representative couldn’t immediately be reached Wednesday. But Jeff Lenard, a spokesman for the National Association of Convenience Stores, questioned whether the legislation would put a dent in city smoking rates, and said it could instead lead to more out-of-state and black market tobacco sales.