Mr. Smith, for one, expressed skepticism that a ban could be enforced. “You don’t know what’s going on in people’s apartment,” he said at the Walt Whitman Houses. He added, “What are they going to do, smell your apartment?”

At the Melrose Houses in the Bronx, Lesli Lino, 25, said that no one in her apartment smoked, but that many residents of her building, including a few on her floor, did.

“It’s horrible,” Ms. Lino said of the odor of smoke that often lingered in elevators and hallways. She said the ban would be a “plus to me.”

Shola Olatoye, the chairwoman and chief executive of Nycha, said, “For us, the major issue is our ability to enforce something like this.” Ms. Olatoye said she had yet to see the proposed rule but expected execution and enforcement to be handled by residents as well as by authority employees.

“It should be resident-led,” she said, adding that the Police Department should not be involved.

Smoking, which is already prohibited in the lobbies and hallways of authority buildings, has already caused friction between tenants and police officers, who have a large presence in many housing projects and are expected to watch out not only for crime but also for violations of authority rules.

Ms. Olatoye noted that in a 2012 residents’ survey conducted by the authority, 14 percent of 1,209 respondents said they smoked, 24 percent said at least one member of their household was a smoker and more than 35 percent said their household included a child with asthma or other respiratory problems.

“There’s clearly a need for addressing this issue head-on,” she said. “The question is, how do we do it?”