But eviction after just one violation "is not grounds for eviction", and smoking on public housing premises is a civil violation, not a crime, the agency said in setting guidelines for local enforcement.
The new policy only applies to all lit tobacco products and does not include e-cigarettes.
Smokers can no longer light up in or near public housing facilities in the USA due to a new rule that went into effect July 31.
Under the terms of the ban, which was passed by the Obama administration in 2016, the use of cigarettes, cigars and pipes is prohibited in all government subsidized housing units.
The rule prohibits smoking in any New York City public housing apartment or building or within 25 feet of the building.
"Eliminating smoking indoors and close to the building is the only way to fully protect people from secondhand smoke".
HUD said the new policy would reduce health hazards from secondhand smoke and encourage residents to quit smoking.
Starting Tuesday, all public housing facilities across the country must have a smoke-free policy in place.
Both HUD and the American Lung Association says it's created to protect the health of people living in federally-funded housing from second-hand smoke.
"We want to make sure that we're providing the best communities that we can for our residents, and so implementing a smoke-free policy is something that falls in line with that", said Keon Montgomery, deputy housing director for the City of Phoenix.
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