The D.C. government plans to sharply increase low-cost housing in some of the District’s most affluent neighborhoods to spread it more equitably throughout the city and correct what officials called a history of “racially discriminatory” housing policies.

In a report released Tuesday, the administration of Mayor Muriel E. Bowser (D) proposes to significantly increase the amount of affordable housing in wealthy parts of the city where it is currently scarce, swaths that include neighborhoods such as Chevy Chase, Spring Valley and Capitol Hill.

The effort would take place on a smaller scale in neighborhoods east of the Anacostia River, which are mostly African American and low-income, and currently account for a disproportionately large share of the city’s low-cost housing.

The report, a copy of which was obtained by The Washington Post, blamed the imbalance on decades of housing policies that it said would take a generation of “focused and sustained effort” to address.

“The current distribution of affordable housing in Washington, DC reflects a legacy of racially discriminatory and exclusionary policies enacted in the past century, and it cannot be corrected overnight,” said the 20-page report by the D.C. Office of Planning. “. . . The whole city has a role in providing affordable housing and access to opportunity to address this legacy, particularly along racial and income lines.”

The plan reflects Bowser’s effort to make housing one of her signature issues. Critics say her administration has encouraged economic development at the expense of longtime residents, who have found themselves priced out of an increasingly expensive city. Low-income residents in the District are being displaced at some of the highest rates in the country, according to a recent study.

The report acknowledges that most of the housing recently built in the District has consisted of small, high-priced rental units, aimed at the young professionals whose influx has transformed neighborhoods and led to class and racial frictions.

But Bowser’s effort is likely to run into several obstacles. It will be costly for the city to provide the financial incentives and vouchers necessary to make it profitable for developers to build such housing. And affluent neighborhoods dominated by single-family homes have long resisted plans to add multifamily buildings with low-cost units. Bowser already faced fierce opposition to an earlier plan to house homeless families in all parts of the city, including legal challenges from residents in Ward 3 and Ward 5. That plan also drew criticism because it didn’t include a family homeless shelter in Ward 2, the richest part of the city.

Office of Planning Director Andrew Trueblood said officials were not ready to specify how much the plan would cost or how it would be implemented. But the report said the city planned to use subsidies, vouchers, expanded land-use incentives and public land partnerships to create the additional units.

On the political front, Bowser’s strategy is to portray the plan as a remedy for social injustice, making it hard for the city’s mostly liberal residents to oppose. At a national housing conference in the District last month, Bowser said NIMBYs — who say “not in my backyard” to affordable housing — could be shamed into supporting it.

“We have to come up with another way to explain what we’re doing that they can embrace,” Bowser said. “Or at least, if they don’t embrace it, they will look shameful.”

The new report sets specific goals for where to locate 12,000 new affordable units that Bowser had previously proposed to create by 2025. They would represent one-third of the 36,000 units she has proposed to build by that year to ease a housing crisis that is also affecting the Washington suburbs, in a pattern typical of economically robust metropolitan areas.

The report defines “affordable housing” as costing no more than 30 percent of household income for households earning less than 80 percent of the Washington-area median family income. That means it would target households earning less than $97,050 a year for a family of four and $67,950 for a single person.

The 12,000 units would be added not only by new construction, but also by providing subsidies or vouchers to preserve the affordability of units that otherwise would become too expensive for low-income residents.

The city’s planning office divides the city geographically into 10 planning areas, and the report specifies the number of affordable units that would be created in each one.

The most dramatic change would take place in the area called Rock Creek West, which includes upscale neighborhoods such as Chevy Chase, Spring Valley and Palisades. There, the number of affordable units would jump by 1,990 units from 470 at present.

The other two planning areas that would have the largest increases are Rock Creek East, in the northern corner of the city, with 1,500 new affordable units, up from 2,650 at present; and Capitol Hill, with 1,400 new units, up from 1,820.

On the other side of the city, in the area called Far Southeast and Southwest, the number would rise by 1,120 units from 15,760 at present. In the other area east of the Anacostia, Far Northeast and Southeast, the number would increase by just 490 units from the current 9,690.

District officials said they decided to concentrate new affordable housing in higher-income communities after hearing from thousands of residents at 24 public events between June and September. More than three-quarters of respondents to a survey said they thought the current distribution was unfair.

“We heard loud and clear that equity was an incredibly important value in the city, and making sure that our neighborhoods are diverse,” Trueblood said.

One of the city’s goals is to break up concentrated poverty, which contributes to a range of social problems, even affecting the academic performance of school-age children, the report said.

“Perhaps most importantly, when low-income residents can move or afford to live in high-opportunity neighborhoods, they thrive,” it said. “Low-income children living in high-opportunity areas are more likely to perform better in the classroom. . . . The benefits continue to accrue as life progresses.”

The D.C. report comes at a time when the region’s planning group, the Metropolitan Washington Council of Governments (COG), and business organizations are pressing the Washington area to intensify efforts to produce more low- and middle-cost housing.

COG voted last month to push local governments to set individual targets to increase production of housing by 75,000 units, or 31 percent over current plans, by 2030. Of those, the group said, at least three-quarters should be affordable for low- and middle-income households.

So far, the District is the only jurisdiction that has committed to a numerical target consistent with the COG plan.