Affordable-housing advocates are divided on the issue, with some saying the focus should be on building more homes rather than on where to enter them. Although many residential buildings in New York integrate low-cost units, developers like Mr. Barnett say that segregating the rentals in a separate part of the building is preferable when market-rate units with the best views and amenities are for sale, and can draw top dollar, in turn allowing them to build more affordable units.

But in the case of the Upper West Side building, that means the poorer tenants will not have access to the pool, the gym, the bowling alley and the private theater, among the add-ons used to entice buyers passing through the nonpoor door. (The renters will have their own laundry room, a community room and bike storage.) There are even separate addresses: 50 Riverside Boulevard for the condominiums, and 470 West 62nd Street for the rentals.

Mr. Barnett’s company built the low-income rentals in exchange for the freedom to construct more square feet than city rules would otherwise allow, a housing strategy called inclusionary zoning. And under current rules, if the developer chooses to attach the affordable segment to the market-rate portion of the project, it is required to provide separate entrances.

But the two-door option, adopted in a minority of new residential projects, is not in keeping with Mr. de Blasio’s liberal political stance, and officials are looking to change a range of housing codes and programs to prohibit them.

“We oppose so-called poor doors and will change the necessary rules so that when affordable housing is provided on-site, we will not allow separate entrances based on income,” Wiley Norvell, a spokesman for the mayor’s office, said.

The lottery process itself may soon be subject to review as well.

A bill introduced last week in the City Council would create a task force to review the lottery system and recommend whether it should be more flexible and undergo other changes. For example, the Council might change the rules so that applicants would not lose their spot in line if their income or family status changes while they are waiting, said Councilman Mark Levine, the sponsor.