Residents of the shelter on the site of the former D.C. General Hospital mingle outside of the facility in the late afternoon. (Michael S. Williamson/The Washington Post)

D.C. Mayor Muriel E. Bowser announced the addresses of seven proposed family homeless shelters Tuesday, setting up a final test of city leaders’ resolve to close the troubled family homeless shelter at D.C. General Hospital.

The mayor’s plan comes almost two years after Relisha Rudd, then 8, disappeared from the shelter in the company of a male city employee and was presumed killed, intensifying scrutiny of D.C. services for the homeless. And it has been one year since the mayor and the D.C. Council agreed to spend $40 million for a network of smaller and more manageable neighborhood shelters as a replacement.

But D.C. residents — including Bowser — have previously fought city efforts to locate homeless families in their neighborhoods, and on Tuesday, Bowser launched a political offensive, saying she was prepared to take head-on any backlash from those who would be asked to be neighbors.

Bowser (D) thinks she may need the momentum. Under a plan devised by Bowser predecessor Vincent C. Gray (D) and now being carried out by Bowser’s office, almost every ward in the city would be asked to take on a shelter, each designed to be a temporary home for as many as 50 families.

Some of the shelters, which could increase the strain on nearby schools and police resources, would be placed in rapidly gentrifying areas. Those shelters include one planned near the U Street corridor and another beside condominiums rising close to Nationals Park. Others, such as the one proposed for a site across the street from the Russian Embassy on Wisconsin Avenue NW, would go into affluent neighborhoods. Poorer areas of Northeast and Southeast Washington, where residents already face widespread underemployment, also would be asked to host shelters.

The plan would solve only a fraction of the city’s homeless crisis, sheltering about a quarter of all families now under city care. The District has more than 700 families in overflow motel rooms across the city and in Maryland, and scores — if not hundreds — most likely would have to remain in such temporary housing long after the new shelters opened, which Bowser said would happen in late 2018.

Laura Green Zeilinger, director of the D.C. Department of Human Services, which oversees services for the homeless, has launched a multiyear overhaul aimed at eventually lowering the number of families needing shelter and allowing the city to transition them from homelessness more quickly.

But on Tuesday, Bowser acknowledged that she could not say when the city might attain that goal. Instead, she cast the neighborhood-based shelter system as a necessary first step in delivering on a major campaign promise to close the D.C. General shelter. “People believe that in a city as prosperous as ours . . . we need to do better by our homeless families,” Bowser said. “I hear it everywhere I go.”

The mayor has been girding for a bruising battle over the plan almost since taking office. For her first year, she refused to have a public discussion of possible locations for the shelters, apparently trying to keep opposition from taking root against any one possibility.

Instead, at nearly every public appearance, her staff has asked residents to sign a pledge to do their part to support neighborhood shelters and the closing of D.C. General. This week, Bowser carefully scripted the plan’s release, first to council members, then to influential community members, finally saying publicly that 12,000 petitioners were behind the effort.

“Do we know that there is going to be pushback block by block? Yes,” said Bowser, who opposed plans to put a large shelter in Ward 4 when she represented that part of the city on the D.C. Council.

On Tuesday, her office released prepared remarks from an Obama administration official lauding the plan.

But there were signs that the fight may not be as bad as Bowser has anticipated.

An overwhelming majority of council members publicly praised the mayor’s plan. Council member Mary M. Cheh (D-Ward 3) said she met with residents Monday night about the shelter proposed along Wisconsin Avenue, not far from the Naval Observatory. Those neighbors, who live in million-dollar homes, expressed a desire to help solve the city’s homeless crisis, she said. “Ward 3 will embrace this,” Cheh said.

In a Washington Post poll in November, nearly 8 in 10 D.C. residents said they would be comfortable with a shelter for 50 homeless families in their neighborhood.

That support included majorities in all eight wards of the city. However, fewer than half in each ward said they would be “very comfortable” having a shelter nearby.

Advocates for homeless families have criticized previously released aspects of Bowser’s plan, including her proposal to build most of the shelters in dormitory style rather than as apartments. They said the communal bathrooms and other shared facilities would perpetuate some of the same unhealthful living conditions that families experience at D.C. General.

On Tuesday, advocates used social media to praise the proposed U Street site, which would have apartment-style housing.

Council member Elissa Silverman (I-At Large) said she visited all but one of the sites in recent days and found that they had uneven access to public transportation and jobs, groceries, and other amenities. Zeilinger said the city plans to offer services at each of the sites.

Council member Kenyan R. McDuffie (D-Ward 5) asked Bowser to reconsider a plan for a shelter on Bladensburg Road NE in his ward, saying the industrial area — with a bus depot and a nightclub nearby — would be a poor fit for homeless residents. He also described the area as having been neglected.

Bowser said she remains open to modifying the plan on the basis of community feedback. In response to McDuffie, who has emerged as a political foe of the mayor’s in recent months, Bowser told reporters, “I didn’t hear him propose an alternative.”

Cost is likely to be among the issues the council will scrutinize. The new shelters would cost an estimated $22 million annually to operate, about $5 million more than the city spends now to keep D.C. General open.

It also is not clear how the city would structure the lease agreement for each shelter.

Officials from the mayor’s office plan to hold simultaneous community meetings at all of the proposed shelter sites Thursday night. The city also will hold a meeting about a women’s shelter that is planned for downtown in Ward 2, the only ward not designated to house a family shelter.

The community meetings are to take place from 6:30 to 8:30 p.m. Thursday at the following locations:

●Ward 1

Anthony Bowen YMCA (conference room), 1325 W St. NW

●Ward 2

One Judiciary Square (old council chambers), 441 Fourth St. NW

●Ward 3

Metropolitan Memorial United Methodist Church, 3401 Nebraska Ave. NW

●Ward 4

Paul Public Charter School (auditorium), 5800 Eighth St. NW

●Ward 5

New Canaan Baptist Church, 2826 Bladensburg Rd. NE

●Ward 6

Friendship Baptist Church, 900 Delaware Ave. SW

●Ward 7

Capitol View Neighborhood Library, 5001 Central Ave. SE

●Ward 8

Matthews Memorial Baptist Church (fellowship hall), 2616 Martin Luther King J. Ave. SE